$A$ 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 ball of mass $10\, kg$ moving with a velocity $10 \sqrt{3} m / s$ along the $x-$axis, hits another ball of mass $20\, kg$ which is at rest. After the collision, first ball comes to rest while the second ball disintegrates into two equal pieces. One piece starts moving along $y-$axis with a speed of $10$ $m / s$. The second piece starts moving at an angle of $30^{\circ}$ with respect to the $x-$axis. The velocity of the ball moving at $30^{\circ}$ with $x-$ axis is $x\, m / s$. The configuration of pieces after collision is shown in the figure below. The value of $x$ to the nearest integer is

A bomb at rest explodes into three fragments $X, Y$ and $Z$. Each one of them has the same mass. Which of the following correctly describes the motion of the fragments?

A sphere of mass $m$, moving with velocity $V$, enters a hanging bag of sand and stops. If the mass of the bag is $M$ and it is raised by height $h$, then the velocity of the sphere was

Two balls at same temperature collide. What is conserved

A particle of mass $m$ moving horizontally with $v_0$ strikes $a$ smooth wedge of mass $M$, as shown in figure. After collision, the ball starts moving up the inclined face of the wedge and rises to $a$ height $h$. When the particle has risen to $a$ height $h$ on the wedge, then choose the correct alternative $(s)$