A bullet weighing $10 \,g$ and moving with a velocity $300 \,m / s$ strikes a $5 \,kg$ block of ice and drop dead. The ice block is kept on smooth surface. The speed of the block after the collision is ........ $cm / s$

$A$ section of fixed smooth circular track of radius $R$ in vertical plane is shown in the figure. $A$ block is released from position $A$ and leaves the track at $B$. The radius of curvature of its trajectory when it just leaves the track at $B$ is:

A projectile is moving at $20\,m/sec$ at its highest point where it breaks into two equal parts due to an internal explosion. One part moves vertically up at $30\,m/sec$ . Then the other part will move at ............. $\mathrm{m}/ \mathrm{s}$

A bomb is projected upwards. At topmost point it explodes in three identical fragments. First fragment comes to ground in $10\  sec$. and others in $20\  sec$ each. Then the height reached by the original bomb is.........$m$

A bullet hits and gets embedded in a solid block resting on a horizontal frictionless table. What is conserved ?

A ball is thrown from $10\,m$ height at speed $v_0$ vertically downward. In colliding  surface of earth it looses $50\%$ of its energy and again reach upto same height. Value  of $v_0$ is :- .................$\mathrm{m}/ \mathrm{s}$