In the figure shown, a particle is released from the position $A$ on a smooth track. When the particle reaches at $B$, then normal reaction on it by the track is .........

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

$A$ $4$ -kilogram disk slides over level ice toward the east at a velocity of $1$ meter per second, as shown. The disk strikes a post and rebounds toward the north at the same speed. The change in the magnitude of the eastward component of the momentum of the disk is ............. $\mathrm{kg}$ $ \cdot $ $\mathrm{m}/ \mathrm{s}$ 

A projectile of mass $M$ is fired so that the horizontal range is $4\, km$. At the highest point the projectile explodes in two parts of masses $M/4$ and $3M/4$ respectively and the heavier part starts falling down vertically with zero initial speed. The horizontal range (distance from point of firing) of the lighter part is .................. $\mathrm{km}$

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 $(s)$

A space craft of mass $'M' $ and moving with velocity $ 'v' $ suddenly breaks in two pieces of same mass $m$. After the explosion one of the mass $ 'm'$  becomes stationary. What is the velocity of the other part of craft