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 :- .................$\mathrm{m}/ \mathrm{s}$

$A$ projectile of mass $"m"$ is projected from ground with a speed of $50 \,m/s$ at an angle of $53^o$ with the horizontal. It breaks up into two equal parts at the highest point of the trajectory. One particle coming to rest immediately after the explosion. The ratio of the radii of curvatures of the moving particle just before and just after the explosion are:

A bomb of mass $12\,\,kg$  at rest explodes into two fragments of masses in the ratio $1 : 3.$  The $K.E.$  of the smaller fragment is $216\,\,J.$  The momentulm of heavier fragment is (in $kg-m/sec$ )

A mass $M$ moving with a certain speed $V$ collides elastically with another stationary mass $m$. After the collision, the masses $M$ and $m$ move with speeds $V^{\prime}$ and $v$, respectively. All motion is in one dimension. Then,

Two balls at same temperature collide. What is conserved

A ball is projected from top of a tower with a velocity of $5\,\, m/s$ at an angle of $53^o$ to horizontal. Its speed when it is at a height of $0.45 \,\,m$ from the point of projection is  ........ $m/s$