JEE Main & Advanced Physics NLM, Friction, Circular Motion Question Bank

done Mock Test - Newtons Laws of Motion With Friction Total Questions - 25

• question_answer1)
  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 clear
  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_answer2)
  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 clear
  B)
  \[\,\tan \,\phi \] done clear
  C)
  \[2\,sin\,\phi \]   done clear
  D)
  \[2\,\cos \,\phi \] done clear
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• question_answer3)
  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 clear
  B)
  \[~45{}^\circ \]     done clear
  C)
  \[37{}^\circ \]               done clear
  D)
  \[30{}^\circ \] done clear
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• question_answer4)
  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 clear
  B)
  \[\frac{{{M}_{2}}}{\mu }-{{M}_{1}}\] done clear
  C)
  \[{{M}_{2}}\,\frac{{{M}_{1}}}{\mu }\]            done clear
  D)
  \[\,\,({{M}_{2}}\,-{{M}_{1}})\mu \] done clear
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• question_answer5)
  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_answer6)
  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 clear
  B)
  0.2      done clear
  C)
  0.3                   done clear
  D)
  0.4 done clear
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• question_answer7)
  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 clear
  B)
   in the first/third quadrants done clear
  C)
   parallel to the y-axis done clear
  D)
   in the second/fourth quadrants done clear
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• question_answer8)
  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 clear
  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_answer9)
  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 clear
  B)
  \[45{}^\circ \]     done clear
  C)
  \[30{}^\circ \]               done clear
  D)
  \[~53{}^\circ \] done clear
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• question_answer10)
  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 clear
  B)
  \[{{t}_{1}}>{{t}_{2}}\] done clear
  C)
  \[{{t}_{2}}>{{t}_{1}}\] done clear
  D)
  \[{{t}_{1}}=2{{t}_{2}}\] done clear
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• question_answer11)
  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 clear
  B)
  4.0 done clear
  C)
  2.0                   done clear
  D)
  2.5 done clear
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• question_answer12)
  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 clear
  B)
  100m done clear
  C)
  1000m done clear
  D)
  800m (Note: It should be minimum distance in which the car can be stopped.) done clear
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• question_answer13)
  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 clear
  B)
  80 N done clear
  C)
  120 N done clear
  D)
  150 N done clear
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• question_answer14)
  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 clear
  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_answer15)
  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 clear
  B)
  \[\frac{20}{2+\sqrt{3}}N\] done clear
  C)
  \[\frac{20}{2-\sqrt{3}}N\]          done clear
  D)
  \[10\,N\] done clear
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• question_answer16)
  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 clear
  B)
  \[W\,\sin \,\alpha \] done clear
  C)
  \[\frac{\sqrt{3}}{2}W\,\sin \,\alpha \]      done clear
  D)
  \[W\sqrt{3}\,\sin \,\alpha \] done clear
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• question_answer17)
  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 clear
  B)
  \[F=\mu Mgf\] done clear
  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_answer18)
  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 clear
  B)
  2 cm done clear
  C)
  4 cm                done clear
  D)
  2.5 cm done clear
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• question_answer19)
  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 clear
  C)
  \[\frac{1}{\sqrt{\mu \alpha }}\]  done clear
  D)
  Infinitesimal done clear
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• question_answer20)
  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_answer21)
  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_answer22)
  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_answer23)
  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_answer24)
  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_answer25)
  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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