$A$ spherical ball of mass $2 \text{ kg}$ falls from a height of $10 \text{ m}$ and is brought to rest after penetrating $10 \text{ cm}$ into sand. The average force exerted by sand on the ball is . . . . . . $\text{N}$. (Take $g = 10 \text{ m/s}^2$)

$A$ body of mass $10\, kg$ is released from a tower of height $20\, m$ and the body acquires a velocity of $10\, m/s$ after falling through the distance $20\, m$. The work done by the air resistance on the body is: ................. $J$ (Take $g = 10\, m/s^2$)

$A$ body is projected vertically upwards with an initial velocity of $7 \, m/s$. At what height will its kinetic energy become half of its initial value (in $, m$)?

$A$ block weighing $20 \ N$ travels down a smooth curved track $AB$ joined to a rough horizontal surface (figure). The rough surface has a friction coefficient of $0.40$ with the block. If the block starts slipping on the track from a point $1.0 \ m$ above the horizontal surface,the distance it will move on the rough surface is: (in $m$)

$A$ particle of mass $2 \,kg$ travels along a straight line with velocity $v = a \sqrt{x}$,where $a$ is a constant. The work done by the net force during the displacement of the particle from $x = 0$ to $x = 4 \,m$ is .........

$A$ chain of length $L$ and mass $m$ is placed upon a smooth surface as shown. The length of the chain on the incline is $b$. Calculate the velocity of the chain when its end reaches point $B$.