The bob of pendulum is projected with horizontal velocity of $\sqrt{3gl},l$ is the length of string. Find the angular displacement of string before it becomes slack.

A particle of mass $m$, attached to the end of a string of length $l$, is released from the initial position $A$, as shown in the figure. The particle moves in a vertical circular path $O.$ When it is vertically below $O,$ the string makes contact with nail $N$ placed directly below $O$ at a distance $h$ and rotates around it. If the particle just completes the vertical circle about $N,$ then 

A block of mass $\sqrt{2} \mathrm{kg}$ is released from the top of an inclined smooth surface as shown in figure. If spring constant of spring is $100 \mathrm{N} {\mathrm{m}}^{-1}$ and block comes to rest after compressing the spring by $1 \mathrm{m},$ then the distance travelled by block before it comes to rest is

Consider the spring block system shown in the figure initially block $m$ is in equilibrium. An impulse gives the block a velocity $v$ upwards. Find the maximum speed of the block during the motion.

A block of mass $m$ is released from a height $h$ from the top of a smooth surface. There is an ideal spring of spring constant $k$ at the bottom of the track. Find the maximum compression in the spring. (Wedge is fixed)