question_answer 1)
A tube of length \[L\] is filled completely with an incompressible liquid of mass \[M\]and closed at both the ends. The tube is then rotated in horizontal plane about one of its ends with a uniform angular velocity \[\omega \]. The force exerted by the liquid at the other end is
A)
\[\frac{ML{{\omega }^{2}}}{2}\] done
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B)
\[ML{{\omega }^{2}}\] done
clear
C)
\[\frac{ML{{\omega }^{2}}}{4}\] done
clear
D)
\[\frac{M{{L}^{2}}{{\omega }^{2}}}{2}\] done
clear
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question_answer 2)
The upper half of an inclined plane with inclination \[\phi \] is perfectly smooth while the lower half is rough. A body starting from rest at the top will again come to rest at the bottom if the coefficient of friction for the lower half is given by
A)
\[2\,\tan \,\phi \] done
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B)
\[\,\tan \,\phi \] done
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C)
\[2\,sin\,\phi \] done
clear
D)
\[2\,\cos \,\phi \] done
clear
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question_answer 3)
A house is built on the top of a hill with \[45{}^\circ \] slope. Due to the sliding of material and sand from top to the bottom of hill, the slope angle has been reduced. If the coefficient of static friction Between sand particles is 0.75, what is the final angle attained by hill? \[(ta{{n}^{-1}}0.75\simeq {{37}^{0}})\]
A)
\[8{}^\circ \] done
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B)
\[~45{}^\circ \] done
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C)
\[37{}^\circ \] done
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D)
\[30{}^\circ \] done
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question_answer 4)
Two blocks of masses \[{{M}_{1}}\] and \[{{M}_{2}}\] are connected with a string passing over a pulley as shown in the figure. The block \[{{M}_{1}}\] lies on a horizontal surface. The coefficient of friction between the block \[{{M}_{1}}\] and the horizontal surface is \[\mu \]. The system accelerates. What additional mass m should be placed on the block \[{{M}_{1}}\] so that the system does not accelerate?
A)
\[\frac{{{M}_{2}}-{{M}_{1}}}{\mu }\] done
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B)
\[\frac{{{M}_{2}}}{\mu }-{{M}_{1}}\] done
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C)
\[{{M}_{2}}\,\frac{{{M}_{1}}}{\mu }\] done
clear
D)
\[\,\,({{M}_{2}}\,-{{M}_{1}})\mu \] done
clear
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question_answer 5)
A block of mass m is at rest with respect to a rough incline kept in elevator moving up With acceleration a. Which of following statements is correct?
A)
The contact force between block and incline is parallel to the incline. done
clear
B)
The contact force between block and incline is of the magnitude \[m(g+a)\]. done
clear
C)
The contact force between block and incline is perpendicular to the incline. done
clear
D)
The contact force is of the magnitude \[mg\,cos\,\theta \] done
clear
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question_answer 6)
A coin is placed at the edge of a horizontal disc rotating about a vertical axis through its axis with a uniform angular speed 2 rad \[{{s}^{-1}}\]. The radius of the disc is 50 cm. Find the minimum coefficient of friction between disc and coin so that the coin does not slip \[(g=10m{{s}^{-2}})\].
A)
0.1 done
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B)
0.2 done
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C)
0.3 done
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D)
0.4 done
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question_answer 7)
Consider the setup of a Ferris wheel in an amusement park. The wheel is turning in a counter clock wise manner. Contrary to the illustration, not all seats are aligned horizontally, i.e., parallel to the x-axis. Determine the orientation of the normal to seat as it passes point A.
A)
parallel to the x-axis done
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B)
in the first/third quadrants done
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C)
parallel to the y-axis done
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D)
in the second/fourth quadrants done
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question_answer 8)
A circular road of radius R is banked for a speed v = 40 km/hr. A car of mass m attempts to go on the circular road, the friction co-efficient between the tyre and road is negligible:
A)
the car cannot make a turn without skidding done
clear
B)
if the car runs at a speed less than 40 km/hr, it will slip up the slope done
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C)
if the car runs at the correct speed of 40 km/hr, the force by the road on the car is equal to \[m{{v}^{2}}/r\] done
clear
D)
if the car runs at the correct speed of 40 km/hr, the force by the road on the car is greater than mg as well as greater than \[m{{v}^{2}}/r\] done
clear
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question_answer 9)
The force required just to move a body up an inclined plane is double the force required just to prevent the body sliding down. If the coefficient of friction is 0.25, the angle of inclination of the plane is
A)
\[37{}^\circ \] done
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B)
\[45{}^\circ \] done
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C)
\[30{}^\circ \] done
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D)
\[~53{}^\circ \] done
clear
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question_answer 10)
A block is placed at the bottom of an inclined plane and projected upwards with some initial speed. It slides up the plane and stops after time \[{{t}_{1}}\]. It begins to slide back down to the bottom in a further time \[{{t}_{2}}\]. The angle of inclination of plane is \[\theta \] and the coefficient of friction between body and the surface is \[\mu \]. Then
A)
\[{{t}_{1}}={{t}_{2}}\] done
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B)
\[{{t}_{1}}>{{t}_{2}}\] done
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C)
\[{{t}_{2}}>{{t}_{1}}\] done
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D)
\[{{t}_{1}}=2{{t}_{2}}\] done
clear
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question_answer 11)
A block rests on a rough inclined plane making an angle of \[30{}^\circ \] with the horizontal. The coefficient of static friction between the block and the plane is 0.8. If the frictional force on the block is 10 N, the mass of the block (in kg) is \[(take\,g=10\,m/{{s}^{2}})\]
A)
1.6 done
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B)
4.0 done
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C)
2.0 done
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D)
2.5 done
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question_answer 12)
Consider a car moving on a straight road with a speed of 100 m/s. The distance at which the car can be stopped is \[[{{\mu }_{k}}=0.5]\]
A)
400m done
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B)
100m done
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C)
1000m done
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D)
800m (Note: It should be minimum distance in which the car can be stopped.) done
clear
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question_answer 13)
Given in the figure are two blocks \[A\] and \[B\] of weight 20 N and 100 N, respectively. These are being pressed against a wall by a force \[F\] as shown. If the coefficient of friction between the blocks is 0.1 and between block B and the wall is 0.15, the frictional force applied by the wall on block \[B\] is
A)
100 N done
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B)
80 N done
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C)
120 N done
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D)
150 N done
clear
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question_answer 14)
The system is pushed by a force \[F\] as shown in figure. All surfaces are smooth except between \[B\] and \[C\]. Friction coefficient between \[B\] and \[C\] is \[\mu \]. Minimum value of \[F\]to prevent block \[B\] from downward slipping is
A)
\[\left( \frac{3}{2\mu } \right)mg\] done
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B)
\[\left( \frac{5}{2\mu } \right)mg\] done
clear
C)
\[\left( \frac{5}{2} \right)\mu mg\] done
clear
D)
\[\left( \frac{3}{2} \right)\mu mg\] done
clear
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question_answer 15)
A block of mass 1 kg is at rest on a horizontal table. The coefficient of static friction between the block and the table is 0.5. The magnitude of the force acting upwards at an angle of \[60{}^\circ \] from the horizontal that will just start the block moving is
A)
\[5\,N\] done
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B)
\[\frac{20}{2+\sqrt{3}}N\] done
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C)
\[\frac{20}{2-\sqrt{3}}N\] done
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D)
\[10\,N\] done
clear
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question_answer 16)
A particle of weight \[W\]rests on a rough inclined plane which makes an angle \[\alpha \] with the horizontal. If the coefficient of static friction \[\mu =2\] tan a, find the horizontal force \[H\] acting transverse to the slope of the plane when the particle is about to slip.
A)
\[2W\,\sin \alpha \] done
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B)
\[W\,\sin \,\alpha \] done
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C)
\[\frac{\sqrt{3}}{2}W\,\sin \,\alpha \] done
clear
D)
\[W\sqrt{3}\,\sin \,\alpha \] done
clear
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question_answer 17)
A body of mass \[M\]is kept on a rough horizontal surface (friction coefficient \[\mu \]). A person is trying to pull the body by applying a horizontal force but the body is not moving. The force by the surface on the body is \[F\], where
A)
\[F=mg\] done
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B)
\[F=\mu Mgf\] done
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C)
\[Mg\le F\le Mg\sqrt{1+{{\mu }^{2}}}\] done
clear
D)
\[Mg\,\ge F\,\ge =\mu Mg\sqrt{1+{{\mu }^{2}}}\] done
clear
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question_answer 18)
A particle describes a horizontal circle in a conical funnel whose inner surface is smooth with speed of 0.5 m/s. What is the height of the plane of circle from vertex of the funnel?
A)
0.25 cm done
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B)
2 cm done
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C)
4 cm done
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D)
2.5 cm done
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question_answer 19)
A long horizontal rod has a bead which can slide along its length, and initially placed at a distance \[L\] from one end \[A\] of the rod. The rod is set in angular motion about \[A\] with constant angular acceleration\[\alpha \]. If the coefficient of friction between the rod and the bead is \[\mu \], and gravity is neglected, then the time after which the bead starts slipping is
A)
\[\sqrt{\frac{\mu }{\alpha }}\] done
clear
B)
\[\frac{\mu }{\sqrt{\alpha }}\] done
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C)
\[\frac{1}{\sqrt{\mu \alpha }}\] done
clear
D)
Infinitesimal done
clear
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question_answer 20)
Three masses of small size are attached by light inextensible strings of various lengths to a point 0 on the ceiling. All of the masses swing round in horizontal circles of various radii with the same angular frequency co (one such circle is drawn in the shown figure). Then pick up the correct statement.
A)
The vertical depth of each mass below point of suspension from ceiling is different. done
clear
B)
The radius of horizontal circular path of each mass is same. done
clear
C)
All masses revolve in the same horizontal plane. done
clear
D)
All the particles must have same mass. done
clear
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question_answer 21)
A block of mass \[M=5\,kg\]is resting on a rough horizontal surface for which the coefficient of friction is 0.2. When a force F= 40 N is applied, what is the acceleration in \[(m/{{s}^{2}})\] of the block? \[(g=10m/{{s}^{2}})\]
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question_answer 22)
A passenger is travelling a train moving at \[40\,m{{s}^{-1}}\]. His suitcase is kept on the berth. The driver of train applies breaks such that the speed of the train decreases at a constant rate to \[20\,m{{s}^{-1}}\] in 5 s. What should be the minimum coefficient of friction between the suitcase and the berth if the suitcase is not to slide during retardation of the train?
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question_answer 23)
A solid block of mass 2 kg is resting inside a cube as shown in the figure. The cube is moving with a velocity \[\vec{v}=5\vec{i}+2\vec{j}\,m{{s}^{-1}}\]. If the coefficient of friction between the surface of cube and block is 0.2, then the force of friction between the block and cube is _______ N.
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question_answer 24)
A block of mass m is lying on a wedge having inclination angle \[\alpha ={{\tan }^{-1}}\left( \frac{1}{5} \right)\]. Wedge is moving with a constant acceleration \[\alpha =2\,m{{s}^{-2}}\]. What is the minimum value of coefficient of friction fi \[\mu \]so that m remains stationary w.r.t. wedge?
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question_answer 25)
A truck is carrying a box of mass m = 50 kg on its flat horizontal rough surface with coefficient of friction \[\mu \] = 0.3. It is crossing a circular track of radius 27 m. What is the maximum speed in (m/s) of the truck so that the box does not slide from the truck while moving on the circular path?
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