A metal ball of mass $2 \mathrm{kg}$ is allowed to fall freely from rest from a height of $5 \mathrm{m}$ above the ground.Calculate the potential energy possessed by the ball when initially at rest. (Given, $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

A hydroelectric power station takes its water from a lake whose water level is at a height of $50 \mathrm{m}$ above the turbine. Assuming an overall efficiency of $40\%$, calculate the mass of water which must flow through the turbine each second to produce power output of $1 \mathrm{MW}$. (Take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

The bob of a simple pendulum is imparted a velocity of $5 \mathrm{m}/\mathrm{s}$ when it is at its mean position. To what maximum vertical height will it rise on reaching at its extreme position if $60\%$ of its energy is lost in overcoming the friction of air? (Take $g=10 \mathrm{m}/{\mathrm{s}}^2$)