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question_answer1)
A ball hits the floor and rebounds after inelastic collision. In this case [IIT 1986]
A)
The momentum of the ball just after the collision is the same as that just before the collision done
clear
B)
The mechanical energy of the ball remains the same in the collision done
clear
C)
The total momentum of the ball and the earth is conserved done
clear
D)
The total energy of the ball and the earth is conserved done
clear
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question_answer2)
A uniform chain of length L and mass M is lying on a smooth table and one third of its length is hanging vertically down over the edge of the table. If g is acceleration due to gravity, the work required to pull the hanging part on to the table is [IIT 1985; MNR 1990; AIEEE 2002; MP PMT 1994, 97, 2000; JIPMER 2000]
A)
\[MgL\] done
clear
B)
\[MgL/3\] done
clear
C)
\[MgL/9\] done
clear
D)
\[MgL/18\] done
clear
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question_answer3)
If \[{{W}_{1}},\,{{W}_{2}}\] and \[{{W}_{3}}\] represent the work done in moving a particle from A to B along three different paths 1, 2 and 3 respectively (as shown) in the gravitational field of a point mass m, find the correct relation between \[{{W}_{1}},\,{{W}_{2}}\] and \[{{W}_{3}}\] [IIT-JEE Screening 2003]
A)
\[{{W}_{1}}>{{W}_{2}}>{{W}_{3}}\] done
clear
B)
\[{{W}_{1}}={{W}_{2}}={{W}_{3}}\] done
clear
C)
\[{{W}_{1}}<{{W}_{2}}<{{W}_{3}}\] done
clear
D)
\[{{W}_{2}}>{{W}_{1}}>{{W}_{3}}\] done
clear
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question_answer4)
A particle of mass m is moving in a horizontal circle of radius r under a centripetal force equal to \[-K/{{r}^{2}}\], where K is a constant. The total energy of the particle is [IIT 1977]
A)
\[\frac{K}{2r}\] done
clear
B)
\[-\frac{K}{2r}\] done
clear
C)
\[-\frac{K}{r}\] done
clear
D)
\[\frac{K}{r}\] done
clear
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question_answer5)
The displacement x of a particle moving in one dimension under the action of a constant force is related to the time t by the equation \[t=\sqrt{x}+3\], where x is in meters and t is in seconds. The work done by the force in the first 6 seconds is [IIT 1979]
A)
9 J done
clear
B)
6 J done
clear
C)
0 J done
clear
D)
3 J done
clear
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question_answer6)
A force \[F=-K(yi+xj)\] (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 particles is [IIT 1998]
A)
\[-2K{{a}^{2}}\] done
clear
B)
\[2K{{a}^{2}}\] done
clear
C)
\[-K{{a}^{2}}\] done
clear
D)
\[K{{a}^{2}}\] done
clear
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question_answer7)
If g is the acceleration due to gravity on the earth's surface, the gain in the potential energy of an object of mass m raised from the surface of earth to a height equal to the radius of the earth R, is [IIT 1983]
A)
\[\frac{1}{2}mgR\] done
clear
B)
2 mgR done
clear
C)
mgR done
clear
D)
\[\frac{1}{4}mgR\] done
clear
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question_answer8)
A lorry and a car moving with the same K.E. are brought to rest by applying the same retarding force, then [IIT 1973; MP PMT 2003]
A)
Lorry will come to rest in a shorter distance done
clear
B)
Car will come to rest in a shorter distance done
clear
C)
Both come to rest in a same distance done
clear
D)
None of the above done
clear
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question_answer9)
A particle free to move along the x-axis has potential energy given by \[U(x)=k[1-\exp {{(-x)}^{2}}]\] for \[-\infty \le x\le +\infty \], where k is a positive constant of appropriate dimensions. Then [IIT-JEE 1999; UPSEAT 2003]
A)
At point away from the origin, the particle is in unstable equilibrium done
clear
B)
For any finite non-zero value of x, there is a force directed away from the origin done
clear
C)
If its total mechanical energy is k/2, it has its minimum kinetic energy at the origin done
clear
D)
For small displacements from x = 0, the motion is simple harmonic done
clear
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question_answer10)
The kinetic energy acquired by a mass m in travelling a certain distance d starting from rest under the action of a constant force is directly proportional to [CBSE PMT 1994]
A)
\[\sqrt{m}\] done
clear
B)
Independent of m done
clear
C)
\[1/\sqrt{m}\] done
clear
D)
m done
clear
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question_answer11)
An open knife edge of mass 'm' is dropped from a height 'h' on a wooden floor. If the blade penetrates upto the depth 'd' into the wood, the average resistance offered by the wood to the knife edge is [BHU 2002]
A)
\[mg\] done
clear
B)
\[mg\left( 1-\frac{h}{d} \right)\] done
clear
C)
\[mg\left( 1+\frac{h}{d} \right)\] done
clear
D)
\[mg{{\left( 1+\frac{h}{d} \right)}^{2}}\] done
clear
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question_answer12)
Consider the following two statements 1. Linear momentum of a system of particles is zero 2. Kinetic energy of a system of particles is zero Then [AIEEE 2003]
A)
1 implies 2 and 2 implies 1 done
clear
B)
1 does not imply 2 and 2 does not imply 1 done
clear
C)
1 implies 2 but 2 does not imply 1 done
clear
D)
1 does not imply 2 but 2 implies 1 done
clear
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question_answer13)
A body is moved along a straight line by a machine delivering constant power. The distance moved by the body in time t is proportional to [IIT 1984; BHU 1984, 95; MP PET 1996; JIPMER 2000; AMU (Med.) 1999]
A)
\[{{t}^{1/2}}\] done
clear
B)
\[{{t}^{3/4}}\] done
clear
C)
\[{{t}^{3/2}}\] done
clear
D)
\[{{t}^{2}}\] done
clear
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question_answer14)
A shell is fired from a cannon with velocity v m/sec at an angle \[\theta \] 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 [IIT 1984; RPET 1999, 2001; UPSEAT 2002]
A)
\[3v\cos \theta \] done
clear
B)
\[2v\cos \theta \] done
clear
C)
\[\frac{3}{2}v\cos \theta \] done
clear
D)
\[\frac{\sqrt{3}}{2}v\cos \theta \] done
clear
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question_answer15)
A vessel at rest explodes into three pieces. Two pieces having equal masses fly off perpendicular to one another with the same velocity 30 meter per second. The third piece has three times mass of each of other piece. The magnitude and direction of the velocity of the third piece will be [AMU (Engg.) 1999]
A)
\[10\sqrt{2}\,m/second\] and \[135{}^\circ \] from either done
clear
B)
\[10\sqrt{2}\,m/second\] and \[45{}^\circ \] from either done
clear
C)
\[\frac{10}{\sqrt{2}}\,m/second\] and \[135{}^\circ \] from either done
clear
D)
\[\frac{10}{\sqrt{2}}\,m/second\] and \[45{}^\circ \] from either done
clear
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question_answer16)
Two particles of masses \[{{m}_{1}}\] and \[{{m}_{2}}\] in projectile motion have velocities \[{{\vec{v}}_{1}}\] and \[{{\vec{v}}_{2}}\] respectively at time t = 0. They collide at time \[{{t}_{0}}\]. Their velocities become \[{{\vec{v}}_{1}}'\] and \[{{\vec{v}}_{2}}'\] at time \[2{{t}_{0}}\] while still moving in air. The value of \[|({{m}_{1}}\overrightarrow{{{v}_{1}}}'\,+{{m}_{2}}\overrightarrow{{{v}_{2}}}')-({{m}_{1}}\overrightarrow{{{v}_{1}}}\,+{{m}_{2}}\overrightarrow{{{v}_{2}}})\]| is [IIT-JEE Screening 2001]
A)
Zero done
clear
B)
\[({{m}_{1}}+{{m}_{2}})g{{t}_{0}}\] done
clear
C)
\[2({{m}_{1}}+{{m}_{2}})g{{t}_{0}}\] done
clear
D)
\[\frac{1}{2}({{m}_{1}}+{{m}_{2}})g{{t}_{0}}\] done
clear
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question_answer17)
Consider elastic collision of a particle of mass m moving with a velocity u with another particle of the same mass at rest. After the collision the projectile and the struck particle move in directions making angles \[{{\theta }_{1}}\]and \[{{\theta }_{2}}\]respectively with the initial direction of motion. The sum of the angles. \[{{\theta }_{1}}+{{\theta }_{2}},\]is [UPSEAT 2004]
A)
\[45{}^\circ \] done
clear
B)
\[90{}^\circ \] done
clear
C)
\[135{}^\circ \] done
clear
D)
\[180{}^\circ \] done
clear
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question_answer18)
A body of mass m moving with velocity v collides head on with another body of mass 2m which is initially at rest. The ratio of K.E. of colliding body before and after collision will be [Roorkee 1982]
A)
1 : 1 done
clear
B)
2 : 1 done
clear
C)
4 : 1 done
clear
D)
9 : 1 done
clear
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question_answer19)
A particle P moving with speed v undergoes a head -on elastic collision with another particle Q of identical mass but at rest. After the collision [Roorkee 2000]
A)
Both P and Q move forward with speed \[\frac{v}{2}\] done
clear
B)
Both P and Q move forward with speed \[\frac{v}{\sqrt{2}}\] done
clear
C)
P comes to rest and Q moves forward with speed v done
clear
D)
P and Q move in opposite directions with speed \[\frac{v}{\sqrt{2}}\] done
clear
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question_answer20)
A set of n identical cubical blocks lies at rest parallel to each other along a line on a smooth horizontal surface. The separation between the near surfaces of any two adjacent blocks is L. The block at one end is given a speed v towards the next one at time \[t=0\]. All collisions are completely inelastic, then [IIT 1995]
A)
The last block starts moving at \[t=\frac{(n-1)L}{v}\] done
clear
B)
The last block starts moving at \[t=\frac{n(n-1)L}{2v}\] done
clear
C)
The centre of mass of the system will have a final speed v done
clear
D)
The centre of mass of the system will have a final speed \[\frac{v}{n}\] done
clear
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