A conveyor belt is moving at a constant speed of $2 \mathrm{m} {\mathrm{s}}^{-1}$. A box is gently dropped on it. The coefficient of friction between them is $0.5$. The distance that the box will move, relative to the belt, before coming to rest on it is $(g=10 \mathrm{m} {\mathrm{s}}^{-2})$

Three blocks $m_1$, $m_2$ and $m_3$ of masses $1.5 \mathrm{kg}, 2.0 \mathrm{kg}$ and $1.0 \mathrm{kg}$, respectively, are placed on a rough surface $(\mu =0.20)$, as shown in the figure. If a force $F$ is applied to give the blocks an acceleration of $3.0 \mathrm{m} {\mathrm{s}}^{-2}$, then the force that the $1.5 \mathrm{kg}$ block exerts on the $2.0 \mathrm{kg}$ block will approximately be

A man of mass $60 \mathrm{kg}$ is standing on a horizontal conveyor belt (see figure). When the belt is given an acceleration of $1 \mathrm{m} {\mathrm{s}}^{-2}$, the man remains stationary with respect to the moving belt. If $g=10 \mathrm{m} {\mathrm{s}}^{-2}$, then the net force acting on the man is

A man of mass $60 \mathrm{kg}$ is standing on a horizontal conveyor belt (see figure). When the belt is given an acceleration of $1 \mathrm{m} {\mathrm{s}}^{-2}$, the man remains stationary with respect to the moving belt. If $g=10 \mathrm{m} {\mathrm{s}}^{-2}$.

Block $A$ has a mass of $2 \mathrm{kg}$ and block $B$ has a mass of $20 \mathrm{kg}$. If the coefficient of kinetic friction between block $B$ and the horizontal surface is $0.1,$ and $B$ is accelerating towards the right with $a=2 \mathrm{m} {\mathrm{s}}^{-2}$, then the mass of block $C$ will be

A block of mass $10 \mathrm{kg}$ is placed at a distance of $5 \mathrm{m}$ from the rear end of a length of a trolley, as shown in the figure. The coefficient of friction between the block and the surface below is $0.2$. Starting from rest, the trolley is given a uniform acceleration of $3 \mathrm{m} {\mathrm{s}}^{-2}$. At what distance from the starting point will the block fall off the trolley? $\left(g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$

A block of mass $2 \mathrm{kg}$ is given a push for a moment, horizontally and then the block starts sliding over a horizontal plane. The graph shows the velocity versus time graph of the motion. The coefficient of sliding friction between the plane and the block is

The friction coefficient between the table and the block, shown in the figure, is $0.2$. The tension in the left string is