Work Energy And Power - Mechanics - Physics Previous Year Questions

The potential energy of an object is $U(x)=\left(5 x^2-4 x^3\right) \mathrm{J}$, where $x$ is the position in metre. The position at which the force becomes zero is

While a person climbs stairs, the gravitational potential energy of the person increases. The source of this energy is

A body of mass 3 kg is moving under the action of a force which causes a displacement of $\left(t^3 / 3\right) \mathrm{m}$, where $t$ is time in seconds. The work done by the force in first 2 sec is

A body is moved along a straight line by an engine which delivers a constant power. The distance moved by the body in time $t$ is proportional to

An engine is dragging a mass of 5000 kg with a velocity of $5 \mathrm{~ms}^{-1}$ along a smooth inclined plane of inclination 1 in 50 . Then the power of the engine is

A ball of mass $m=1 \mathrm{~kg}$ is thrown from the top of a building with initial velocity $\mathbf{v}=(20 \mathrm{~m} / \mathrm{s}) \hat{\mathbf{i}}+(24 \mathrm{~m} / \mathrm{s}) \hat{\mathbf{j}}$ at time $t=0$. The change in the potential energy of the ball between $t=0$ and $t=6 \mathrm{~s}$, if the ball does not hit the ground, then (assume, $g=10 \mathrm{~m} \mathrm{~s}^2$ )

A force $\mathbf{F}=(2 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}) \mathrm{N}$ is applied on an object of mass $M$. What is the work done by this force in moving the object horizontally along the $X$-axis by 3 m ?

When a body is acted upon by a resultant force, then the work done by the resultant force is equal to

A force acts on a body of mass 10 kg , resulting in its displacement given as $x=\left(\frac{t^3}{25}\right) \mathrm{m}$, where $t$ is the time in seconds. The work done by the force in 5 s is

A ball of mass 1 kg moves in a straight line with velocity $v=c x^\alpha$, where $c=1$ (SI unit) and $\alpha$ is a constant. If the work done by the net force during its displacement from $x=0$ to $x=4 \mathrm{~m}$ is 128 J , then the $\alpha$ is

A pump on the ground floor of a building can pump up water to fill a tank of volume $36 \mathrm{~m}^3$ in 30 min . If the tank is 50 m above the ground, and the electric power consumed by the pump is 40 k W , the efficiency of the pump is

(use $g=10 \mathrm{~m} / \mathrm{s}^2$ and density of water $=1000 \mathrm{~kg} / \mathrm{m}^3$ )

A boat of mass 1000 kg goes from rest to speed 20.0 $\mathrm{m} / \mathrm{s}$ in 5.0 s . The water exerts a constant drag force and the acceleration of the boat is constant. If the average power required by the boat is 45000 W , then the magnitude of the drag force is

Statement I The slope of kinetic energy-displacement curve of a body in motion will be directly proportional to its acceleration.

Statement II From a height of 15 m , a ball is projected vertically upwards with a velocity of $30 \mathrm{~m} / \mathrm{s}$. If the ball rises to the same height after hitting the ground, the loss of its energy on hitting the ground is $30 \%$.

Statement III The velocity acquired by a body of mass $m$ after travelling a fixed distance from rest under the action of a constant force is directly proportional to mass $m$.

Which of the following is correct?

An object is moving in a straight line under the influence of a source of constant power. If $v$ and $t$ are velocity and time respectively, then

Under action of force, a 2 kg body moves such that its position $x$ as function of time $t$ is given by $x=\alpha t^2 / 2$, where $x$ is in metre, $t$ is in seconds and $\alpha=1 \mathrm{~m} / \mathrm{s}^2$. The work done by the force in the first two seconds is

The block starts from rest as shown in the figure. Find the work done by force of 10 N and friction in the time 0 to 4 s . [Take, $g=10 \mathrm{~m} / \mathrm{s}^2$ ]

A force of 4 N acts on a 10 kg body initially at rest. Let $W_1$ is work done by force during $0 \leq t \leq \mathrm{ls}$. Likewise $W_2$ is the work done by force during $\mathrm{l} \mathrm{s} \leq t \leq 2 \mathrm{~s}$, where $t$ is time in second. The ratio $\frac{W_2}{W_1}$ is

An elevator of mass 500 kg is ascending upwards with a constant acceleration $a=2 \mathrm{~m} / \mathrm{s}^2$. What is the work done by the tension in the elevator cable during its climb by 12 m ? (Take, $g=10 \mathrm{~m} / \mathrm{s}^2$ )