$A$ pump on the ground floor of a building can pump up water to fill a tank of volume $36 \,m^3$ in $30 \,min$. If the tank is $50 \,m$ above the ground, and the electric power consumed by the pump is $40 \,kW$, the efficiency of the pump is (Use $g=10 \,m / s^2$ and density of water $=1000 \,kg / m^3$ ) (in $\%$)

$A$ particle moves with a velocity $\vec v = 6\hat i - 4\hat j + 3\hat k \, m/s$ under the influence of a constant force $\vec F = 20\hat i + 15\hat j - 5\hat k \, N$. The instantaneous power applied to the particle is ......... $J/s$.

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 elevator can carry a maximum load of $1800 \; kg$ (elevator $+$ passengers) and is moving up with a constant speed of $2 \; m s^{-1}$. The frictional force opposing the motion is $4000 \; N$. Determine the minimum power delivered by the motor to the elevator in watts as well as in horsepower.

$A$ body of mass $m$ is accelerated uniformly from rest to a speed $v$ in a time $T$. The instantaneous power delivered to the body as a function of time is given by

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?