In the figure,two blocks $M$ and $m$ are tied together with an inextensible and light string. The mass $M$ is placed on a rough horizontal surface with coefficient of friction $\mu$ and the mass $m$ is hanging vertically against a smooth vertical wall. The pulley is frictionless. When the downward acceleration of the elevator becomes equal to $g$,then

  • A
    both the blocks remain stationary with respect to the elevator
  • B
    both the blocks accelerate vertically downwards with $g$ with respect to ground
  • C
    the tension in the string becomes equal to zero
  • D
    All of the above

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$A$ block $A$ with mass $100\, kg$ is resting on another block $B$ of mass $200\, kg$. As shown in the figure,a horizontal rope tied to a wall holds block $A$. The coefficient of friction between $A$ and $B$ is $0.2$,while the coefficient of friction between $B$ and the ground is $0.3$. The minimum required force $F$ to start moving block $B$ will be ........ $N$.

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Consider the following statements $A$ and $B$ and identify the correct answer given below:
$(A)$ $A$ body initially at rest is acted upon by a constant force. The rate of change of its kinetic energy varies linearly with time.
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$A$ block of mass $m$ is on an inclined plane of angle $\theta$. The coefficient of friction between the block and the plane is $\mu$ and $\tan \theta > \mu$. The block is held stationary by applying a force $P$ parallel to the plane. The direction of force pointing up the plane is taken to be positive. As $P$ is varied from $P_1 = mg(\sin \theta - \mu \cos \theta)$ to $P_2 = mg(\sin \theta + \mu \cos \theta)$,the frictional force $f$ versus $P$ graph will look like:

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