$A$ quarter horsepower motor runs at a speed of $600 \ rpm$. Assuming $60 \%$ efficiency,the work done by the motor in one rotation is (in $J$)

$A$ motor pump lifts $6$ tonnes of water from a well of depth $25 \ m$ to the first floor of height $35 \ m$ from the ground floor in $20$ minutes. The power of the pump (in $kW$) is: $[g=10 \ ms^{-2}]$

Two men have a weight ratio of $5 : 3$. If the ratio of the time taken by them to climb stairs is $11 : 9$,find the ratio of their power.

$A$ body of mass $1 \ kg$ begins to move under the action of a time-dependent force $\vec{F} = (t \hat{i} + 3t^2 \hat{j}) \ N$,where $\hat{i}$ and $\hat{j}$ are the unit vectors along the $x$ and $y$ axes. The power developed by the above force at time $t = 2 \ s$ will be $.............. \ W$.

From a waterfall,water is falling down at the rate of $100 \ kg/s$ on the blades of a turbine. If the height of the fall is $100 \ m$,then the power delivered to the turbine is approximately equal to ........... $kW$.

The velocity $v$ reached by a car of mass $m$ at a certain distance from the starting point,driven with constant power $P$,is such that: