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question_answer1)
A ball whose kinetic energy is E, is projected at an angle of \[45{}^\circ \] to the horizontal. The kinetic energy of the ball at the highest point of its flight will be
A)
E done
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B)
\[E/\sqrt{2}\] done
clear
C)
\[E/2\] done
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D)
zero done
clear
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question_answer2)
A load hangs from a travelling crane, moving horizontally with velocity v. If the load is not to swing more than 4 m horizontally, when the crane is stopped suddenly, what is the maximum allowable speed of the crane?
A)
4.05 m/s done
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B)
4.00 m/s done
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C)
3.00 m/s done
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D)
3.50 m/s done
clear
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question_answer3)
A 10 kg block is pulled in the vertical plane along a frictionless surface in the form of an arc of a circle of radius 10 m. The applied force is of 200 N as shown in figure. If the block had started from rest at A, the velocity at B would be
A)
1.7 m/s done
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B)
17 m/s done
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C)
27 m/s done
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D)
34 m/s done
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question_answer4)
Calculate the work done on the tool by \[\vec{F}\left( 11.25\hat{i}+11.25\hat{j} \right)N\] if the tool is first moved out along the x-axis to the point \[x=3.00m,\] \[y=0\] and then moved parallel to the y-axis to\[x=3.00m,\]\[y=3.00\text{ }m\].
A)
67.5 J done
clear
B)
85 J done
clear
C)
102 J done
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D)
7.5 J done
clear
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question_answer5)
A force F acting on an object varies with distance x as shown here. The force is in N and x in m. The work done by the force in moving the object from \[x=0\] to \[x=6\] m is
A)
18.0 J done
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B)
13.5 J done
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C)
9.0 J done
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D)
4.5 J done
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question_answer6)
A particle describe a horizontal circle of radius 0.5 m with uniform speed. The centripetal force acting is 10 N. The work done in describing a semicircle is
A)
zero done
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B)
5J done
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C)
\[5\pi J\] done
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D)
\[10\,\pi J\] done
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question_answer7)
A force F acts on a particle such that its position x changes as shown in the figure. The work done by the particle as it moves from \[x=0\] to 20 m is
A)
37.5 J done
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B)
10 J done
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C)
45 J done
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D)
22.5 J done
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question_answer8)
Two identical beads of \[m=100\] gram are connected by an inextensible massless string can slide along the two arms AC and BC of a rigid smooth wire frame in a vertical plane. If the system is released from rest, the kinetic energy of the first particle when they have moved by a distance of 0.1 m is\[8 \times {{10}^{-3}}J\]. Find the value of \[\operatorname{x}.\left( g=10m/{{s}^{2}} \right)~~~~~~\]
A)
8 done
clear
B)
6 done
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C)
9 done
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D)
11 done
clear
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question_answer9)
A cord is used to lower vertically a block of mass M, a distance d at a constant downward acceleration of\[g/4\]. The work done by the cord on the block is
A)
\[Mg\frac{d}{4}\] done
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B)
\[3Mg\frac{d}{4}\] done
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C)
\[-3Mg\frac{d}{4}\] done
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D)
\[Mgd\] done
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question_answer10)
A spring of spring constant \[5\times 103 N/m\] is stretched initially by 5 cm from the upstretched position. Then the work required to stretch it further by another 5 cm is
A)
18.75 J done
clear
B)
25.00 J done
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C)
6.25 J done
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D)
12.50 J done
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question_answer11)
A uniform force of \[\left( 3\hat{i}+\hat{k} \right)\] newton acts on a article of mass 2 kg. The particle is displaced from position \[\left( 2\hat{i}+\hat{k} \right)\] meter to position \[\left( 4\hat{i}+3\hat{j}-\hat{k} \right)\] meter. The work done by the force on the particle is
A)
6 J done
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B)
13 J done
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C)
15 J done
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D)
9 J done
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question_answer12)
The position of a particle of mass 4 g, acted upon by a constant force is given by\[\operatorname{x} = 4{{t}^{2}} + t\], where x is in metre and t in second. The work done during the first 2 seconds is
A)
\[128mJ\] done
clear
B)
\[512mJ\] done
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C)
\[576mJ\] done
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D)
\[144mJ\] done
clear
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question_answer13)
A body moves a distance of 10 m along a straight line under the action of a force of 5 newtons. If the work done is 25 joules, the angle which the force makes with the direction of motion of body is
A)
\[0{}^\circ \] done
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B)
\[30{}^\circ \] done
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C)
\[60{}^\circ \] done
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D)
\[90{}^\circ \] done
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question_answer14)
A block of mass m is suspended by a light thread from a lift. The lift is moving upward with uniform velocity v. From the frame of lift, the work done by tension on the block in t seconds will be
A)
\[-mgvt\] done
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B)
\[0\] done
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C)
\[\frac{mgvt}{2}\] done
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D)
\[mgvt\] done
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question_answer15)
The work done by a force\[\vec{F}=\left( -6{{x}^{3}}\hat{i} \right)N,\]in displacing a particle from \[x=4\text{ }m\text{ }to\text{ }x=-2\]m is
A)
\[360J\] done
clear
B)
\[240J\] done
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C)
\[-240J\] done
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D)
\[-360J\] done
clear
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question_answer16)
Work done by static friction on an object
A)
May be positive done
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B)
must be negative done
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C)
Must be zero done
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D)
None of these done
clear
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question_answer17)
A particle is placed at the origin and a force \[F=kx\] is acting on it (where k is positive constant). If\[U(0)=0\], the graph of \[U(x)\]versus x will be (where U is the potential energy function)
A)
B)
C)
D)
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question_answer18)
Calculate the K.E and RE. of the ball half way up, when a ball of mass 0.1 kg is thrown vertically upwards with an initial speed of \[20\text{ }m{{s}^{-1}}\].
A)
\[10\text{ }J,\text{ }20\text{ }J\] done
clear
B)
\[10\,J,\text{ }10\,J\] done
clear
C)
\[15\text{ }J,\text{ }8\text{ }J\] done
clear
D)
\[8\,J,16\,J\] done
clear
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question_answer19)
At time \[t=0s\] particle starts moving along the x-axis. If its kinetic energy increases uniformly with time f, the net force acting on it must be proportional to
A)
\[\sqrt{t}\] done
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B)
constant done
clear
C)
\[t\] done
clear
D)
\[\frac{1}{\sqrt{t}}\] done
clear
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question_answer20)
Two bodies of masses 4 kg and 5 kg are moving with equal momentum. Then the ratio of their respective kinetic energies is
A)
\[4:5\] done
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B)
\[2:1\] done
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C)
\[1:3\] done
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D)
\[5:4\] done
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question_answer21)
A rod of mass m and length (is made to stand at an angle of \[60{}^\circ \] with the vertical. Potential energy of the rod in this position is
A)
\[mg\,\ell \] done
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B)
\[\frac{mg\,\ell }{2}\] done
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C)
\[\frac{mg\,\ell }{3}\] done
clear
D)
\[\frac{mg\,\ell }{4}\] done
clear
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question_answer22)
A 2 kg block slides on a horizontal floor with a speed of4m/s. It strikes a uncompressed spring, and compresses it till the block is motionless. The kinetic friction force is 15N and spring constant is 10,000 N/m. The spring compresses by Critical Thinking
A)
8.5 cm done
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B)
5.5 cm done
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C)
2.5 cm done
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D)
11.0 cm done
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question_answer23)
The potential energy of a conservative system is given by\[\operatorname{U} = a{{y}^{2}}-by\], where y represents the position of the particle and a as well as b are constants. What is the force acting on the system?
A)
\[-ay\] done
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B)
\[-by\] done
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C)
\[2ay-b\] done
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D)
\[\operatorname{b}-2ay\] done
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question_answer24)
A block of mass \[m=0.1\] kg is connected to a spring of unknown spring constant k. It is compressed to a distance \[\left( \frac{x}{2} \right)\] from its equilibrium position and released from rest. After approaching half the distance from equilibrium position, it hits another block and comes to rest momentarily, while the other block moves with a velocity\[3m{{s}^{-1}}\]. The total initial energy of the spring is
A)
\[0.3\text{ }J\] done
clear
B)
\[0.6\text{ }J\] done
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C)
\[0.8\text{ }J\] done
clear
D)
\[1.5\text{ }J\] done
clear
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question_answer25)
A block of 1 kg is kept on a rough surface of an elevator moving up with constant velocity of 5m/s. In 10 seconds work done by normal reaction (the block does not slide on the inclined surface)
(i) from ground frame is 320 J |
(ii) is equal to work done by friction force in elevator frame |
(iii) is equal to work done by friction in ground frame of the three statements given above, the one that is true is given by the choice |
A)
Only (i) done
clear
B)
(ii) and (iii) done
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C)
(i) and (ii) done
clear
D)
only (iii) done
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question_answer26)
300 J of work is done in sliding a 2 kg block up an inclined plane of height 10m. Taking\[g=10m/{{s}^{2}}\], work done against friction is
A)
100J done
clear
B)
zero done
clear
C)
1000J done
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D)
200J done
clear
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question_answer27)
A force acts on a 30gm particle in such a way that the position of the particle as a function of time is given by\[x=3t-4{{t}^{2}}+{{t}^{3}}\], where x is in metres and t is in seconds. The work done during the first 4 seconds is
A)
576mJ done
clear
B)
450mJ done
clear
C)
490mJ done
clear
D)
530mJ done
clear
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question_answer28)
A man starts walking from a point on the surface of earth (assumed smooth) and reaches diagonally opposite point. What is the work done by him?
A)
Zero done
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B)
Positive done
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C)
Negative done
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D)
Nothing can be said done
clear
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question_answer29)
The components of a force acting on a particle are varying according to the graphs shown. When the particles move from (0,5,6) to (2,10,0) then the work done by this force is
A)
192J done
clear
B)
\[\frac{400}{3}J\] done
clear
C)
\[\frac{287}{2}J\] done
clear
D)
None of these done
clear
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question_answer30)
A force \[\operatorname{F}=- K \left( y\hat{i} + x\hat{j} \right)\] (where K is a positive constant) acts on a particle moving in the xy plane. Starting from the origin, the particle is taken along the positive x axis to the point (a, 0), and then parallel to the y axis to the point (a, a). The total work done by the force F on the particle is
A)
\[- 2K{{a}^{2}}\] done
clear
B)
\[2K{{a}^{2}}\] done
clear
C)
\[- K{{a}^{2}}\] done
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D)
\[K{{a}^{2}}\] done
clear
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question_answer31)
A block of mass 1 kg is pulled along the curve path ACB by a tangential force as shown in figure. The work done by the frictional force when the block moves from A to B is
A)
5 J done
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B)
10 J done
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C)
20 J done
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D)
None of these done
clear
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question_answer32)
If stretch in a spring of force constant k is tripled then the ratio of elastic potential energy in the two cases will be
A)
9:1 done
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B)
1:6 done
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C)
3:1 done
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D)
1:3 done
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question_answer33)
One man takes 1 min. to raise a box to a height of 1 metre and another man takes 1/2 min. to do so. The energy of the
A)
Two is different done
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B)
two is same done
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C)
first is more done
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D)
second is more done
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question_answer34)
If the momentum of a body is increased by 50%, then the percentage increase in its kinetic energy
A)
50% done
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B)
100% done
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C)
125% done
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D)
200% done
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question_answer35)
A ball dropped from a height of 2m reaches to a height of 1.5m before hitting the ground. Then the percentage of potential energy lost is
A)
25 done
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B)
30 done
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C)
50 done
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D)
100 done
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question_answer36)
A body starts from rest and acquires a velocity V in time T. The work done on the body in time t will be proportional to
A)
\[\frac{V}{T}t\] done
clear
B)
\[\frac{{{V}^{2}}}{T}{{t}^{2}}\] done
clear
C)
\[\frac{{{V}^{2}}}{{{T}^{2}}}t\] done
clear
D)
\[\frac{{{V}^{2}}}{{{T}^{2}}}{{t}^{2}}\] done
clear
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question_answer37)
Four particles given, have same momentum. Which has maximum kinetic energy
A)
Proton done
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B)
Electron done
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C)
Deutron done
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D)
a-particles done
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question_answer38)
A running man has half the kinetic energy of that of a boy of half of his mass. The man speeds up by 1m/s so as to have same K.E. as that of the boy. The original speed of the man will be
A)
\[\sqrt{2}m/s\] done
clear
B)
\[\left( \sqrt{2}-1 \right)m/s\] done
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C)
\[\frac{1}{\left( \sqrt{2}-1 \right)}m/s\] done
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D)
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question_answer39)
A steel ball of mass 5g is thrown downward with velocity 10 m/s from height 19.5 m. It penetrates sand by 50 cm. The change in mechanical energy will be
A)
1 J done
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B)
1.25 J done
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C)
1.5 J done
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D)
1.75 J done
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question_answer40)
The figure gives the potential energy function U(x) for a system in which a particle is in one- dimensional motion. In which region the magnitude of the force on the particle is greatest:
A)
OA done
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B)
AB done
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C)
BC done
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D)
CD done
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question_answer41)
A ball is allowed to fall from a height of 10 m. If there is 40% loss of energy due to air friction, then velocity of the ball when it hit the ground is
A)
\[\sqrt{190}m/s\] done
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B)
\[\sqrt{180}m/s\] done
clear
C)
\[\sqrt{150}m/s\] done
clear
D)
\[\sqrt{120}m/s\] done
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question_answer42)
A body falls freely under gravity. Its velocity is v when it has lost potential energy equal to U. What is the mass of the body?
A)
\[{{\operatorname{U}}^{2}}/{{v}^{2}}\] done
clear
B)
\[2{{\operatorname{U}}^{2}}/{{v}^{2}}\] done
clear
C)
\[2\operatorname{U}/{{v}^{2}}\] done
clear
D)
\[\operatorname{U}/{{v}^{2}}\] done
clear
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question_answer43)
When a body is projected vertically up from the ground with certain velocity, its potential energy and kinetic energy at a point A are in the ratio 2 : 3. If the same body is projected with double the previous velocity, then at the same point A the ratio of its potential energy to kinetic energy is
A)
9 : 1 done
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B)
2 : 9 done
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C)
1 : 9 done
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D)
9 : 2 done
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question_answer44)
A uniform chain of length 2 m and mass 0.1 kg overhangs a smooth table with its two third part lying on the table. Find the kinetic energy of the chain as it completely slips- off the table.
A)
\[\frac{8}{9}J\] done
clear
B)
\[\frac{12}{5}J\] done
clear
C)
\[\frac{3}{7}J\] done
clear
D)
\[\frac{11}{3}J\] done
clear
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question_answer45)
A 1 kg particle at a height of 8m has a speed of 1 Om/s down a fixed incline making an angle \[53{}^\circ \] with horizontal as shown in figure. It slides on a horizontal section of length 10 m at ground level and then up a fixed incline making an angle \[37{}^\circ \] with horizontal. All surfaces have\[{{\mu }_{k}} = 0.5\]. How far (in meters) from point 0 (bottom of right inclined plane), along the incline making an angle \[37{}^\circ \] with horizontal, does the particle first come to rest?
A)
1m done
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B)
0.5m done
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C)
2m done
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D)
5m done
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question_answer46)
A man places a chain of mass m and length L on a table slowly. Initially the lower end of the chain just touches the table. The man drops the chain when half of the chain is in vertical position. Then work done by the man in this process is
A)
\[-mg\frac{L}{2}\] done
clear
B)
\[-\frac{mg\,L}{4}\] done
clear
C)
\[-\frac{3mg\,L}{8}\] done
clear
D)
\[-\frac{mg\,L}{8}\] done
clear
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question_answer47)
. A particle of mass 10 g moves along a circle of radius 6.4 cm with a constant tangential acceleration. What is the magnitude of this acceleration if the kinetic energy of the particle becomes equal to \[8\times 1{{0}^{-4}}J\]by the end of the second revolution after the beginning of the motion?
A)
\[0.1 m/{{s}^{2}}\] done
clear
B)
\[0.15 m/{{s}^{2}}\] done
clear
C)
\[0.18 m/{{s}^{2}}\] done
clear
D)
\[0.2 m/{{s}^{2}}\] done
clear
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question_answer48)
A variable force P is maintained tangent to a frictionless cylindrical surface of radius a as shown in figure. By slowly varying this force, a block of weight W is moved and the spring to which it is stretched from position 1 to position 2. The work done by the force P is
A)
\[\operatorname{W} a sin \theta \] done
clear
B)
\[\frac{1}{2} k{{a}^{2}} {{\theta }^{2}}\] done
clear
C)
\[\operatorname{W}\,a\,sin \theta + k\,{{a}^{2}}{{\theta }^{2}}\] done
clear
D)
\[\operatorname{W}\,a\,sin \theta +\frac{1}{2} k\,{{a}^{2}}{{\theta }^{2}}\] done
clear
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question_answer49)
A straight bar, of mass 15 kg and length 2 m, at rest on a frictionless horizontal surface, receives an instantaneous impulse of 7.5 Ns perpendicular to the bar. If the impulse is applied at the mid-point of the bar, the energy transferred is
A)
3.2 J done
clear
B)
1.9J done
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C)
3.8 J done
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D)
2.5 J done
clear
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question_answer50)
A particle, which is constrained to move along the x-axis, is subjected to a force in the same direction which varies with the distance x of the particle from the origin as\[\operatorname{F}\left( x \right)=-\operatorname{kx}+a{{x}^{3}}\]. Here k and a are positive constants. For\[x\ge 0\], the functional form of the potential energy U(x) of the particle is
A)
B)
C)
D)
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question_answer51)
Two blocks of masses m and M are joined with an ideal spring of spring constant k and kept on a rough surface as shown. The spring is initially unstretched and the coefficient of friction between the blocks and the horizontal surface is u. What should be the maximum speed of the block of mass M such that the smaller block does not move?
A)
\[\mu g\sqrt{\frac{Mm}{\left( M+m \right)k}}\] done
clear
B)
\[\mu g\sqrt{\frac{\left( M+m \right)k}{Mm}}\] done
clear
C)
\[\mu g\sqrt{\frac{\left( 2M+m \right)m}{kM}}\] done
clear
D)
None of these done
clear
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question_answer52)
Two blocks of masses \[{{m}_{1}}=10\,kg\,\,and\,\,{{m}_{2}}=20\,\,kg\] are connected by a spring of stiffness\[k=200N/m\]. The coefficient of friction between the blocks ' and the fixed horizontal surface is\[\mu = 0.1\]. Find the minimum constant horizontal force F (in newtons) to be applied to m, in order to slide the mass my \[\left[ Take g = 10 m/{{s}^{2}} \right]\]
A)
\[\mu {{m}_{1}}g+\frac{\mu {{m}_{2}}g}{2}\] done
clear
B)
\[\mu {{m}_{1}}g+\mu {{m}_{2}}g\] done
clear
C)
\[\mu {{m}_{1}}g+\frac{\mu {{m}_{2}}g}{2}\] done
clear
D)
\[\frac{\mu {{m}_{1}}g+\mu {{m}_{2}}g}{2}\] done
clear
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question_answer53)
Two objects each of mass m are connected with a uniform rope having same mass m and length \[\ell =10/3\] m are shown in the figure. The rope can slide on a frictionless pulley which is fixed to the edge of the table. Initially 1/3 of the rope hangs vertically. Friction is negligible everywhere.
If the system is released from rest and object on the right hand side descend further by a distance of 1/3, what would be the speed of the object (in m/s)?
A)
2.12 m/s done
clear
B)
3.33 m/s done
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C)
0.33 m/s done
clear
D)
4.12 m/s done
clear
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question_answer54)
A bead of mass m is sliding down the fixed inclined rod without friction. It is connected to a point P on the horizontal surface with a light spring of spring constant k. The bead is initially released from rest and the spring is initially unstressed and vertical. The bead just stops at the bottom of the inclined rod. Find the angle which the inclined rod makes with horizontal.
A)
\[{{\cot }^{-1}}\left( 1+\sqrt{\frac{2mg}{kh}} \right)\] done
clear
B)
\[ta{{n}^{-1}}\left( 1+\sqrt{\frac{2mg}{kh}} \right)\] done
clear
C)
\[{{\cot }^{-1}}\left( 1+\sqrt{\frac{mg}{kh}} \right)\] done
clear
D)
\[ta{{n}^{-1}}\left( 1+\sqrt{\frac{mg}{kh}} \right)\] done
clear
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question_answer55)
A body of mass m is accelerated uniformly from rest to a speed v in a time T. The instantaneous power delivered to the body as a function of time is given by
A)
\[\frac{m{{v}^{2}}}{{{T}^{2}}}.{{t}^{2}}\] done
clear
B)
\[\frac{m{{v}^{2}}}{{{T}^{2}}}.t\] done
clear
C)
\[\frac{1}{2}\frac{m{{v}^{2}}}{{{T}^{2}}}.{{t}^{2}}\] done
clear
D)
\[\frac{1}{2}\frac{m{{v}^{2}}}{{{T}^{2}}}.t\] done
clear
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question_answer56)
A car of mass m starts from rest and accelerates so that the instantaneous power delivered to the car has a constant magnitude pg. The instantaneous velocity of this car is proportiourl to:
A)
\[{{\operatorname{t}}^{2}}{{p}_{o}}\] done
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B)
\[{{\operatorname{t}}^{1/2}}\] done
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C)
\[{{\operatorname{t}}^{-1/2}}\] done
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D)
\[\frac{t}{\sqrt{m}}\] done
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question_answer57)
How much water, a pump of 2 kW can raise in one minute to a height of 10 m, take\[\operatorname{g} = 10 m/{{s}^{2}}\]?
A)
1000 done
clear
B)
1200 done
clear
C)
100 done
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D)
2000 done
clear
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question_answer58)
In figure, a block having a mass of 5 kg is released from rest, where the spring acting on the body are horizontal and have a tension of 50 N. The force constant of each spring is, \[k=500\text{ }N/m\]. The velocity of the block after it has descended by 0.3m.
A)
0 done
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B)
I m/s done
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C)
2 m/s done
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D)
none done
clear
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question_answer59)
The engine of a vehicle delivers constant power. If the vehicle is moving up the inclined plane then, its velocity,
A)
Must remain constant done
clear
B)
Must increase done
clear
C)
Must decrease done
clear
D)
May increase, decrease or remain same. done
clear
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question_answer60)
A body is moved along a straight line by a machine delivering a constant power. The distance moved by the body in time 'f' is proportional to
A)
\[{{t}^{3/4}}\] done
clear
B)
\[{{t}^{3/2}}\] done
clear
C)
\[{{t}^{1/4}}\] done
clear
D)
\[{{t}^{1/2}}\] done
clear
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question_answer61)
A body projected vertically from the earth reaches a height equal to earth's radius before returning to the earth. The power exerted by the gravitational force is greatest
A)
At the highest position of the body done
clear
B)
At the instant just before the body hits the earth done
clear
C)
It remains constant all through done
clear
D)
At the instant just after the body is projected done
clear
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question_answer62)
A body of mass 10 kg moves with a velocity v of 2m/s along a circular path of radius 8 m. The power produced by the body will be
A)
10J/s done
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B)
98J/s done
clear
C)
49J/s done
clear
D)
zero done
clear
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question_answer63)
A constant power P is applied to a car starting from rest. If v is the velocity of the car at time t, then
A)
\[v\propto t\] done
clear
B)
\[v\propto \frac{1}{t}\] done
clear
C)
\[v\propto \sqrt{t}\] done
clear
D)
\[v\propto \frac{1}{\sqrt{t}}\] done
clear
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question_answer64)
If two persons A and B take 2 seconds and 4 seconds respectively to lift an object to the same height h, then the ratio of their powers is
A)
1:2 done
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B)
1:1 done
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C)
2:1 done
clear
D)
1:3 done
clear
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question_answer65)
A 10 H.P. motor pumps out water from a well of depth 20 m and fills a water tank of volume 2380 litres at a height of 10 m from the ground. The running time of the motor to fill the empty water tank is \[\left( g= 10m{{s}^{-2}} \right)\]
A)
5 minutes done
clear
B)
10 minutes done
clear
C)
15 minutes done
clear
D)
20 minutes done
clear
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question_answer66)
If a machine gun fires n bullets per second each with kinetic energy K, then the power of the machine gun is
A)
\[{{\operatorname{nK}}^{2}}\] done
clear
B)
\[\frac{K}{n}\] done
clear
C)
\[{{\operatorname{n}}^{2}}K\] done
clear
D)
\[\operatorname{nK}\] done
clear
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question_answer67)
A ring of mass m can slide over a smooth vertical rod as shown in figure. The ring is connected to a spring of force constant\[k=4mg\text{ }I\text{ }R\], where 2 R is the natural length of the spring. The other end of spring is fixed to the ground at a horizontal distance 2 R from the base of the rod. If the mass is released at a height 1.5 R, then the velocity of the ring as it reaches the ground is Critical Thinking
A)
\[\sqrt{gR}\] done
clear
B)
\[2\sqrt{gR}\] done
clear
C)
\[\sqrt{2gR}\] done
clear
D)
\[\sqrt{3gR}\] done
clear
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question_answer68)
An engineer claims to have made an engine delivering 10kW power with fuel consumption of 1 g/s. The calorific value of fuel is 2 kcal/g. This claim is
A)
Valid done
clear
B)
Invalid done
clear
C)
Depends on engine design done
clear
D)
Dependent on load done
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question_answer69)
A force applied by an engine of a train of mass \[2.05\times 1{{0}^{6}} kg\]changes its velocity from 5m/s to 25 m/s in 5 minutes. The power of the engine is
A)
1.025 MW done
clear
B)
2.05 MW done
clear
C)
5 MW done
clear
D)
6 MW done
clear
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question_answer70)
A 10 m long iron chain of linear mass density \[0.8 kg {{m}^{-1}}\] is hanging freely from a rigid support. If\[\operatorname{g}~=10 m{{s}^{-2}}\], then the power required to left the chain up to the point of support in 10 second
A)
10 W done
clear
B)
20 W done
clear
C)
30 W done
clear
D)
40 W done
clear
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question_answer71)
The net power of all the forces acting on a particle (P) versus time curve is shown. Work done upon the particle from A to B
A)
Increases done
clear
B)
Decreases done
clear
C)
First increases then done
clear
D)
First decreases then done
clear
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question_answer72)
A wind-powered generator converts wind energy into electrical energy. Assume that the generator converts a fixed fraction of the wind energy intercepted by its blades into electrical energy For wind speed v, the electrical power output will be proportional to
A)
v done
clear
B)
\[{{v}^{2}}\] done
clear
C)
\[{{v}^{3}}\] done
clear
D)
\[{{v}^{4}}\] done
clear
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question_answer73)
A body of mass 1 kg begins to move under the action of a time dependent force\[\vec{F}=\left( 2t\hat{i}+3{{t}^{2}}\hat{j} \right]) N,\], where \[\hat{i} and \hat{j}\]are unit vectors alogn x and y axis. What power will be developed by the force at the time t?
A)
\[\left( 2{{t}^{2}}+3{{t}^{3}} \right)W\] done
clear
B)
\[\left( 2{{t}^{2}}+4{{t}^{4}} \right)W\] done
clear
C)
\[\left( 2{{t}^{3}}+3{{t}^{4}} \right)W\] done
clear
D)
\[\left( 2{{t}^{3}}+3{{t}^{5}} \right)W\] done
clear
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question_answer74)
The energy content of gasoline is\[3.6\times 1{{0}^{7}}J/L\]. A motor with an efficiency of 20% is needed at fall output power of 45 kW for 50.0 minutes. How many litres of gasoline are required to operate the motor for this amount of time?
A)
0.31 L done
clear
B)
0.38 L done
clear
C)
1.6 L done
clear
D)
19 L done
clear
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question_answer75)
An escalator has 2400 W of power available to move passengers from the first floor of a mall to the second, 6.0 m vertically. If the average mass of the passengers is 65 kg, what is the maximum number of passengers that can be carried to the second floor in 1.0 minute?
A)
4 done
clear
B)
5 done
clear
C)
22 done
clear
D)
37 done
clear
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question_answer76)
An iron ball of mass m, suspended by a light inextensible string of length from a fixed point, 0, is shifted by an angle \[{{\theta }_{0}}\] as shown so as to strike the vertical wall perpendicularly. The ' maximum angle made by the string with vertical after the first collision, if e is the coefficient of restitution, is
A)
\[{{\sin }^{-1}}\left\{ 1-{{e}^{2}}\left( 1-\cos {{\theta }_{0}} \right) \right\}\] done
clear
B)
\[{{\cos }^{-1}}\left\{ 1-{{e}^{2}}\left( 1-\cos {{\theta }_{0}} \right) \right\}\] done
clear
C)
\[{{\tan }^{-1}}\left\{ 1-{{e}^{2}}\left( 1-\cos {{\theta }_{0}} \right) \right\}\] done
clear
D)
Zero done
clear
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question_answer77)
Mass \[{{m}_{1}}\] strikes m which is at rest. The ratio of masses for which they will collide again (collision between ball and wall are elastic, coefficient of restitution between \[{{\operatorname{m}}_{1}} and {{m}_{2}}\]is e and all the surfaces are smooth.)
A)
\[<\frac{e}{2+e}\] done
clear
B)
\[>\frac{2e}{2+e}\] done
clear
C)
\[\ge \frac{e}{2\left( 2+e \right)}\] done
clear
D)
None of the above done
clear
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question_answer78)
Three masses m, 2m and 3m are moving in x-y plane with speed 3u, 2u and u respectively as shown in figure. The three masses collide at the same point at P and stick together. The velocity of resulting mass will be
A)
\[\frac{u}{12}\left( \hat{i}+\sqrt{3}\hat{j} \right)\] done
clear
B)
\[\frac{u}{12}\left( \hat{i}-\sqrt{3}\hat{j} \right)\] done
clear
C)
\[\frac{u}{12}\left( -\hat{i}+\sqrt{3}\hat{j} \right)\] done
clear
D)
\[\frac{u}{12}\left( -\hat{i}-\sqrt{3}\hat{j} \right)\] done
clear
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question_answer79)
Two small bodies of masses 'm' and '2m' are placed in a fixed smooth horizontal circular hollow tube of mean radius 'r' as shown. The mass 'm' is moving with speed 'u' and the mass '2m' is stationary. After their first collision, the time elapsed for next collision is [ coefficient of restitution e = 1/2 ]
A)
\[\frac{2\pi r}{u}\] done
clear
B)
\[\frac{4\pi r}{u}\] done
clear
C)
\[\frac{3\pi r}{u}\] done
clear
D)
\[\frac{12\pi r}{u}\] done
clear
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question_answer80)
A block lying on a smooth surface with spring connected to it is pulled by an external force as shown. Initially the velocity of ends A and B of the spring are 4 m/s and 2 m/s respectively. If the energy of the spring is increasing at the rate of 20 J/sec, then the stretch in the spring is Critical Thinking
A)
1.0 cm done
clear
B)
2.0 cm done
clear
C)
10 cm done
clear
D)
2.0 cm done
clear
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question_answer81)
A car of weight W is on an inclined road that rises by 100 m over a distance of 1 Km and applies a constant frictional force \[\frac{W}{20}\] on the car. While moving uphill on the road at a speed of\[10\text{ }m{{s}^{-1}}\], the car needs power P. If it needs power \[\frac{P}{2}\] while moving downhill at speed v then value of v is:
A)
\[20m{{s}^{-1}}\] done
clear
B)
\[5m{{s}^{-1}}\] done
clear
C)
\[15m{{s}^{-1}}\] done
clear
D)
\[10m{{s}^{-1}}\] done
clear
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question_answer82)
A block of mass \[m=1\text{ }kg\]is moving with a constant acceleration \[a=1\text{ }m/{{s}^{2}}\]on a rough horizontal plane. The coefficient of friction between the block and plane is\[u=0.1\]. The initial velocity of block is zero at\[t=0\]. The power delivered by the external agent at a time t = 2 sec from the beginning is equal to \[\left( Takeg= 10m/{{s}^{2}} \right)\]
A)
1 watt done
clear
B)
2 watt done
clear
C)
3 watt done
clear
D)
4 watt done
clear
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question_answer83)
A ball of mass m hits the floor making an angle 9 as shown in the figure. Ife is the coefficient of restitution, then which relation is true, for the velocity component before and after collision?
A)
\[{{V}^{1}}\sin \theta '=V\,sin\theta \] done
clear
B)
\[{{V}^{1}}\sin \theta '=-\,sin\theta \] done
clear
C)
\[{{V}^{1}}\cos \theta '=V\,\cos \theta \] done
clear
D)
\[{{V}^{1}}\cos \theta '=-V\,\cos \theta \] done
clear
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question_answer84)
A rubber ball is dropped from a height of 5m on a plane, where the acceleration due to gravity is not shown. On bouncing it rises 1.Sm. The ball loses its velocity on bouncing by a factor of
A)
\[\frac{16}{25}\] done
clear
B)
\[\frac{2}{5}\] done
clear
C)
\[\frac{3}{5}\] done
clear
D)
\[\frac{9}{25}\] done
clear
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question_answer85)
A ball of mass m moving with a constant velocity strikes against a ball of same mass at rest. If e= coefficient of restitution, then what will be the ratio of velocity of two balls after collision?
A)
\[\frac{1-e}{1+e}\] done
clear
B)
\[\frac{e-1}{e+1}\] done
clear
C)
\[\frac{1+e}{1-e}\] done
clear
D)
\[\frac{2+e}{e-1}\] done
clear
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question_answer86)
The block of mass M moving on the frictionless horizontal surface collides with the spring of spring constant k and compresses it by length L. The maximum momentum of the block after collision is
A)
\[\frac{k{{L}^{2}}}{2M}\] done
clear
B)
\[\sqrt{Mk}L\] done
clear
C)
\[\frac{M{{L}^{2}}}{k}\] done
clear
D)
zero done
clear
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question_answer87)
An object of mass 2.0 kg makes an elastic collision with another object of mass M at rest and continues to move in the original direction but with one-fourth of its original speed. What is the value of M?
A)
0.75kg done
clear
B)
1.0kg done
clear
C)
1.2kg done
clear
D)
None of these done
clear
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question_answer88)
A bullet of mass 20g and moving with 600 m/s collides with a block of mass 4 kg hanging with the string. What is velocity of bullet when it comes out of block, if block rises to height 0.2 m after collision?
A)
200mA done
clear
B)
150 m/s done
clear
C)
400 m/s done
clear
D)
300 m7s done
clear
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question_answer89)
A block of mass 0.50 kg is moving with a speed of \[2.00\text{ }m{{s}^{-1}}\] on a smooth surface. It strikes another mass of 1.00 kg and then they move together as a single body. The energy loss during the collision is
A)
0.16 J done
clear
B)
1.00 J done
clear
C)
0.67 J done
clear
D)
0.34 J done
clear
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question_answer90)
The heart of man pumps 5 liters of blood through the arteries per minute at a pressure of 150 mm of mercury. If the density of mercury be \[13.6\times 1{{0}^{3}}kg/{{m}^{3}}\]and \[\operatorname{g} = 10m/{{s}^{2}}\]then the power of heart in watt is:
A)
2.35 done
clear
B)
3.0 done
clear
C)
1.50 done
clear
D)
1.70 done
clear
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question_answer91)
An engine is hauling a train of mass M kg on a level track at a constant speed v m/s. The resistance due to friction is\[fN/kg\]. What extra power must the engine develop to maintain the speed up a gradient of h in s :
A)
\[\frac{mghv}{s}\] done
clear
B)
\[\frac{mghs}{v}\] done
clear
C)
\[Mghvs\] done
clear
D)
zero done
clear
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question_answer92)
An electric pump is used to fill an overhead tank of capacity \[9{{m}^{3}}\] kept at a height of 10m above the ground. If the pump takes 5 minutes to fill the tank by consuming 10 kW power the efficiency of the pump should be \[\left( g = 10 m{{s}^{-2}} \right)\]
A)
60% done
clear
B)
40% done
clear
C)
20% done
clear
D)
30% done
clear
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question_answer93)
Water falls from a height of 60 m at the rate of 15 kg/s to operate a turbine. The losses due to frictional force are 10% of energy. How much power is generated by the turbine?\[\left( g = 10 m/{{s}^{2}} \right)\]
A)
8.1 k W done
clear
B)
10.2 kW done
clear
C)
12.3 k W done
clear
D)
7.0 kW done
clear
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question_answer94)
A particle of mass m is moving in a circular path of constant radius r such that its centripetal acceleration \[{{a}_{c}}\] is varying with time t as \[{{a}_{c}}={{k}^{2}}r{{t}^{2}}\] where k is a constant. The power delivered to the particles by the force acting on it is
A)
\[2\pi m{{k}^{2}}{{r}^{2}}t\] done
clear
B)
\[m{{k}^{2}}{{r}^{2}}t\] done
clear
C)
\[\frac{\left( m{{k}^{4}}{{r}^{2}}{{t}^{5}} \right)}{3}\] done
clear
D)
zero done
clear
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question_answer95)
A uniform rope of linear mass density 'k and length (. is coiled on a smooth horizontal surface. One end is pulled up with constant velocity v. Then the average power applied by the external agent in pulling the entire rope just off the horizontal surface is
A)
\[\frac{1}{2}\lambda \ell {{v}^{2}}+\frac{\lambda {{\ell }^{2}}g}{2}\] done
clear
B)
\[\lambda \ell gv\] done
clear
C)
\[\frac{1}{2}\lambda {{v}^{3}}+\frac{\lambda \ell vg}{2}\] done
clear
D)
\[\lambda \ell vg+\frac{1}{2}\lambda {{v}^{3}}\] done
clear
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question_answer96)
A particle fells from a height A on a fixed horizontal plane and rebounds. If e is the coefficient of restitution, the total distance travelled by the particle before it stops rebounding is
A)
\[\frac{h}{2}\frac{\left[ 1-{{e}^{2}} \right]}{\left[ 1+{{e}^{2}} \right]}\] done
clear
B)
\[\frac{h\left[ 1-{{e}^{2}} \right]}{\left[ 1+{{e}^{2}} \right]}\] done
clear
C)
\[\frac{h}{2}\frac{\left[ 1+{{e}^{2}} \right]}{\left[ 1-{{e}^{2}} \right]}\] done
clear
D)
\[\frac{h\left[ 1+{{e}^{2}} \right]}{\left[ 1-{{e}^{2}} \right]}\] done
clear
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question_answer97)
A collision occurs between two identical balls of mass m each, moving with velocity\[{{\overrightarrow{\mu }}_{1}}\,and\,{{\overrightarrow{\mu }}_{2}}\]. If the collision is head on and the energy lost in the collision is \[\Delta E=\frac{3}{16}{{({{\vec{u}}_{1}}-{{\vec{u}}_{2}})}^{2}}\] then the coefficient of restitution is
A)
0.25 done
clear
B)
0.75 done
clear
C)
0.5 done
clear
D)
0.9 done
clear
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question_answer98)
A massive disc of radius R is moved with a constant velocity m on a frictionless table. Another small disc collides with it elastically with a speed of\[{{v}_{0}}= 0.3 m/s\], the velocities of the discs being parallel. The distance (/shown in the figure is equal to R/2, friction between the discs is negligible. For which u (in m/s) will the small disc move perpendicularly to its original motion after the collision?
A)
0.1 done
clear
B)
0.5 done
clear
C)
1.0 done
clear
D)
0.01 done
clear
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question_answer99)
A shell is fired from a cannon with a velocity v (m/sec.) at an angle 9 with the horizontal direction. At the highest point in its path it explodes into two pieces of equal mass. One of the pieces retraces its path to the cannon and the speed (in m/sec.) of the other piece immediately after the explosion is
A)
\[3\,v\,cos\text{ }\theta \] done
clear
B)
\[2\,v\,cos\text{ }\theta \] done
clear
C)
\[\frac{3}{2}\,v\,cos\text{ }\theta \] done
clear
D)
\[\sqrt{\frac{3}{2}}\,v\,cos\text{ }\theta \] done
clear
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question_answer100)
An object of mass m is projected vertically upwards with a speed of \[{{v}_{0}}\]At the same moment another object of mass M, which is initially above the projected one, is dropped from a height of h. The two point like objects collide completely in elastically, and they stick to each other. Find kinetic energy (in J) of combined mass just before it hits the ground.\[(Given : m = 1 kg, {{v}_{0}}= 20 m/s,\] \[M=3 kg, h=20m,g= 10m/{{s}^{2}})\]
A)
550 J done
clear
B)
650 J done
clear
C)
450 J done
clear
D)
250 J done
clear
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