A bag is gently dropped on a conveyor belt moving at a speed of $2 \mathrm{m} {\mathrm{s}}^{-1}$. The coefficient of friction between the conveyor belt and bag is $0.4$. Initially, the bag slips on the belt before it stops due to friction. The distance travelled by the bag on the belt during slipping motion is : [Take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$]

Two inclined planes are placed as shown in figure.
A block is projected from the Point $A$ of inclined plane $AB$ along its surface with a velocity just sufficient to carry it to the top Point $B$ at a height $10 \mathrm{m}$. After reaching the Point $B$ the block slides down on inclined plane $BC$. Time it takes to reach to the point $C$ from point $A$ is $t\left(\sqrt{2}+1\right)\mathrm{s}$. The value of t is _____ (use $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

A uniform metal chain of mass $m$ and length $L$ passes over a massless and frictionless pulley. It is released from rest with a part of its length $l$ is hanging on one side and rest of its length $L-l$  is hanging on the other side of the pulley. At a certain point of time, when $l=\frac{L}{x}$, the acceleration of the chain is $\frac{g}{2}$. The value of $x$ is _____.

A smooth circular groove has a smooth vertical wall as shown in figure. A block of mass $m$ moves against the wall with a speed $v$. Which of the following curve represents the correct relation between the normal reaction on the block by the wall $\left(N\right)$ and speed of the block $\left(v\right)$?