The work-energy theorem is valid in the presence of:

$A$ body is released from a height of $30 \ m$ vertically downwards. The speed of the body at which potential energy is twice that of kinetic energy is (Acceleration due to gravity $= 10 \ m \ s^{-2}$)

The mass of a pendulum bob is $50 \ gm$. The bob is released from a horizontal position $A$ as shown in the figure. If the length of the pendulum is $1.5 \ m$,what will be its kinetic energy when it reaches the lowest point $B$ of its path? (Take $g = 10 \ m/s^2$)

$A$ bullet of mass $10 \; g$ leaves a rifle at an initial velocity of $1000 \; m/s$ and strikes the earth at the same level with a velocity of $500 \; m/s$. The work done in joule $(J)$ in overcoming the resistance of air will be:

$A$ car comes to rest after traveling a distance $s$ under a constant retarding force $F$. If the mass of the car is increased by $50\%$,at what distance will the car come to rest,assuming the same retarding force $F$ and initial velocity $v$?

$A$ 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 $g = 10 \text{ m/s}^2$)