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

$A$ force $\vec{F} = (4 \hat{i} + \hat{j} - 2 \hat{k}) \text{ N}$ acting on a body maintains its velocity at $\vec{v} = (2 \hat{i} + 2 \hat{j} + 3 \hat{k}) \text{ m s}^{-1}$. The power exerted is $..... \text{ W}$.

An elevator in a building can carry a maximum of $10$ persons,with the average mass of each person being $68 \; kg$. The mass of the elevator itself is $920 \; kg$ and it moves with a constant speed of $3 \; m/s$. The frictional force opposing the motion is $6000 \; N$. If the elevator is moving up with its full capacity,the power delivered by the motor to the elevator $\left(g = 10 \; m/s^{2}\right)$ must be at least .............. $W$.

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?

$A$ weightlifter lifts a weight of $300\; kg$ to a height of $2\; m$ from the ground in $3\; s$. The average power generated by him is.....$W$.

$A$ 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: $[g=10 \ ms^{-2}]$