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

A small body slips, subject to the force of friction, from point $A$ to point $B$ along two curved surfaces of equal radius, first along route $1,$ then along route $2$. Friction does not depend on the speed and the coefficient of friction on both routes is the same. In which case will the body’s speed at $B$ be greater?

A cylinder of mass $10\,kg$ is sliding on a plane with an initial velocity of $10\,m/s$. If coefficient of friction between surface and cylinder is $ 0.5$, then before stopping it will describe ............. $\mathrm{m}$

A block of mass $15 \;kg$ is placed on a long trolley. The coefficient of static friction between the block and the trolley is $0.18$. The trolley accelerates from rest with $0.5 \;m s ^{-2}$ for $20 \;s$ and then moves with uniform velocity. Discuss the motion of the block as vlewed by

$(a)$ a stationary observer on the ground,

$(b)$ an observer moving with the trolley.

A body of mass $2 \,kg$ is kept by pressing to a vertical wall by a force of $100\, N$. The coefficient of friction between wall and body is $0.3.$ Then the frictional force is equal to ........ $N$

A $1.0 kg$ block of wood sits on top of an identical block of wood, which sits on top of a flat level table made of plastic. The coefficient of static friction between the wood surfaces is $\mu_1$, and the coefficient of static friction between the wood and plastic is $\mu_2$. Ahorizontal force $F$ is applied to the top block only, and this force is increased until the top block starts to move. The bottom block will move with the top block if and only if