$A$ pump is required to lift $1000 \, kg$ of water per minute from a well of depth $10 \, m$ and eject it with a speed of $10 \, m/s$. The horsepower of the engine needed is: (Assume $g = 10 \, m/s^2$)

An object of mass $m$ is projected with an initial velocity $u$ at an angle $\theta$ with the horizontal. What is the average power delivered by gravity in reaching the highest point?

$A$ quarter horsepower motor runs at a speed of $600 \text{ r.p.m.}$ Assuming $40\%$ efficiency,the work done by the motor in one rotation will be:

$A$ body of mass $2 \ kg$ is initially at rest. It starts moving unidirectionally under the influence of a source of constant power $P$. Its displacement in $4 \ s$ is $\frac{1}{3} \alpha^2 \sqrt{P} \ m$. The value of $\alpha$ will be $.............$

An object of mass $1000 \ g$ experiences a time-dependent force $\vec{F} = (2t \hat{i} + 3t^2 \hat{j}) \ N$. The power generated by the force at time $t$ is

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.