Power

Water falls down a $500.0 \mathrm{m}$ shaft to reach a turbine which generates electricity. How much water must fall per second in order to generate $1.00\times {10}^9$ watts of power ? (Assume $50\%$ efficiency of conversion and $g=10 \mathrm{m} {\mathrm{s}}^{-1}$)

A girl of mass $50 \mathrm{kg}$ swinging on a cradle. If she moves with a velocity of $2 \mathrm{m} {\mathrm{s}}^{-1}$ upwards in a direction making an angle $60°$ with the vertical, then the power generated is $\left(g=9.8 \mathrm{m} {\mathrm{s}}^{-2}\right)$

A body is initially at rest. It undergoes one-dimensional motion with constant acceleration. The power delivered to it at time $t$ is proportional to:

An engine develops $10 \mathrm{kW}$ of power. The time it will take in lifting a mass of  $200 \mathrm{kg}$ to a height of $40 \mathrm{m}. (\mathrm{g}=10 \mathrm{m}/{\mathrm{s}}^2)$ is:

Water falls from a height of  $60 \mathrm{m}$ at the rate of  $15 \mathrm{kg}/\mathrm{s}$ to operate a turbine. The losses due to frictional forces are $10\%$  of energy. How much power is generated by the turbine? $(\mathrm{g}=10 \mathrm{m}/{\mathrm{s}}^2)$.

A tube-well pumps out $2400 \mathrm{kg}$ of water per $\mathrm{minute}$. If the water is coming out with a velocity of $3 \mathrm{m} {\mathrm{s}}^{-1}$, then the power of the pump is

An engine pumps up $1000 \mathrm{kg}$ of coal from a mine $100 \mathrm{m}$ deep in $0.5 \sec$. The pump is running with diesel and efficiency of diesel engine is $25\%$. Then its power consumption will be $\left(g=10 \mathrm{m} {\sec }^{-2}\right)$

A block of mass $m$ slides along the horizontal track with kinetic friction $\mu .$ A man pulls the block through a light rope which makes an angle $\mathrm{\theta }$ with the horizontal as shown in the figure. The tension in the light rope is $T$ as shown. The block moves with constant speed $v$. Power delivered by the man to the block is 

A force $\overrightarrow{F}=(3\hat{\mathrm{i}}+4\hat{\mathrm{j}}) \mathrm{N}$ acts on a $2 \mathrm{kg}$ movable object that moves from an initial position $\overrightarrow{d_{\mathrm{i}}}=(-3\hat{\mathrm{i}}-2\hat{\mathrm{j}}) \mathrm{m}$ to a final position $\overrightarrow{d_{\mathrm{f}}}=(5\hat{\mathrm{i}}+4\hat{\mathrm{j}}) \mathrm{m}$ in $6 \mathrm{s}$. The average power delivered by the force during the interval is equal to

A box is moved along a straight line by a machine delivering constant power. The distance traversed by the body in time $t$ is proportional to

What is the force acting on the particle? if the kinetic energy $K$ of a particle moving in a straight line depends on the distance $s$ as $K = a{s}^2.$

(where $a$ is a constant)

A particle of mass $M$ is moving in a circle of fixed radius $R$ in such a way that its centripetal acceleration at time $t$ is given by $n^{2}R{t}^2$ where $n$ is a constant. The power delivered to the particle by the force acting on it is:

An elevator can carry a maximum load of $1000 \mathrm{kg}$ is moving up with a constant speed of $2 \mathrm{m} {\mathrm{s}}^{-1}$. The frictional force opposing the motion is $2000 \mathrm{N}$. The minimum power delivered by the motor to the elevator is (Assuming $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

The position $\left(x\right)$ of a body moving along x-axis at time $\left(t\right)$ is given by $\mathrm{x}=3{\mathrm{t}}^2,$where $x$ is in metre and $t$ is in second. If mass of body is $2 \mathrm{kg},$ then find the instantaneous power delivered to body by force acting on it at $t=4 \mathrm{s} :-$

An elevator of mass $500 \mathrm{kg}$ is to be lifted up at a constant velocity of $0.4 \mathrm{m} {\mathrm{s}}^{-1}$. What should be the minimum horse power of the motor to be used? (Take $\mathrm{g}=10 \mathrm{m} {\mathrm{s}}^{-2}$ and $1 hp=750$watts $):-$

Velocity of a body of mass $2 \mathrm{kg}$ moving in xy plane is given by $\overrightarrow{\mathrm{v}}=\left(2\hat{\mathrm{i}}+4\mathrm{t}\hat{\mathrm{j}}\right) \mathrm{m} {\mathrm{s}}^{-1}$, where $t$ is the time in second. The power delivered to the body by the resultant force acting on it at $t=5 \mathrm{s}$ is

How much energy does a 100w electric bulb produce in 1 min?

A block of mass $m$ slides along the track with kinetic friction $\mathrm{\mu }$. A man pulls the block through a rope which makes an angle $\mathrm{\theta }$ with the horizontal as shown in the figure. The block moves with constant speed $v$. Power delivered by man is

A particle is projected at $\mathrm{t}=0$ from a point on the ground with certain velocity at an angle with the horizontal. The power of gravitation force is plotted against time. Which of the following is the best representation?

What is the power of the engine if it changes the velocity of a  $2.05\times {10}^6 \mathrm{Kg}$ train from $5 \mathrm{m} {\mathrm{s}}^{-1}$ to $25\mathrm{ }\mathrm{m} {\mathrm{s}}^{-1}$ in $5\mathrm{ }\mathrm{minutes}$ ?