Water falls down a $500.0 \,m$ shaft to reach a turbine which generates electricity. How many $m^3$ of water must fall per second in order to generate $1.00 \times 10^9 \,W$ of power? (Assume $50 \%$ efficiency of conversion and $g=10 \,ms^{-2}$)

$A$ $750 \,W$ motor drives a pump which lifts $300 \,L$ of water per minute to a height of $6 \,m$. The efficiency of the motor is nearly (Take,acceleration due to gravity to be $10 \,m/s^2$) (in $\%$)

$1\,kWh$ is a unit of power. This statement is true or false? If it is wrong,then correct it.

$A$ body of mass $m$ starts from rest and moves with uniform acceleration such that it attains a velocity $v$ in time $T$. The instantaneous power delivered to the body as a function of time $t$ is given by:

$A$ man $M_1$ of mass $80 \ kg$ runs up the stairs with a box in $15 \ s$. Another man $M_2$ of the same mass $80 \ kg$ runs up the same stairs with the same box in $20 \ s$. Find the ratio of the power generated by them.

An electric pump is used to fill an overhead tank of capacity $9\,m^3$ kept at a height of $10\,m$ above the ground. If the pump takes $5\,minutes$ to fill the tank by consuming $10\,kW$ power,the efficiency of the pump should be : ............... $\%$ (Take $g = 10\,m/s^2$)