Work, Power & Energy — JEE Main PYQs

The potential energy ( U ) of a diatomic molecule is a function dependent on r (interatomic distance) as $\mathrm{U}=\frac{\alpha }{{\mathrm{r}}^{10}}-\frac{\beta }{{\mathrm{r}}^5}-3$
Where, $\alpha$ and $\beta$ are positive constants. The equilibrium between two atoms will be …

A small bob tied at one end of a thin string of length 1 m is describing a vertical circle so that the maximum and minimum tension in the string are in the ratio $5:1$. The velocity of the bob at the highest position is ____ $\mathrm{m}/\mathrm{s}.($ Take …

A porter lifts a heavy suitcase of mass 80 kg and at the destination lowers it down by a distance of 80 cm with a constant velocity. Calculate the work done by the porter in lowering the suitcase.
(take $\mathrm{g}=9.8{\mathrm{ms}}^{-2}$)

Two persons A and B perform same amount of work in moving a body through a certain distance d with application of forces acting at angle $45^{\circ }$ and $60^{\circ }$ with the direction of displacement respectively. The ratio of force applied by person $A$ to the force appl …

A cord is wound round the circumference of wheel of radius $r$. The axis of the wheel is horizontal and the moment of inertia about it is I . A weight mg is attached to the cord at the end. The weight falls from rest. After falling through a distance ' h ', the square of angular …

A boy is rolling a 0.5 kg ball on the frictionless floor with the speed of $20{\mathrm{ms}}^{-1}$. The ball gets deflected by an obstacle on the way. After deflection it moves with $5\%$ of its initial kinetic energy. What is the speed of the ball now?

A pendulum bob has a speed of $3\mathrm{m}/\mathrm{s}$ at its lowest position. The pendulum is 50 cm long. The speed of bob, when the length makes an angle of $60^{\circ }$ to the vertical will be $(\mathrm{g}=10\mathrm{m}/{\mathrm{s}}^2)$ ____ $\mathrm{m}/\mathrm{s}$.

A force of $F=(5y+20)\hat{j}$ N acts on a particle. The work done by this force when the particle is moved from $y=0$ m to $y=10$ m is _____ J.

An automobile of mass '$m$' accelerates starting from origin and initially at rest, while the engine supplies constant power P. The position is given as a function of time by:

Given below is the plot of a potential energy function $\mathrm{U}(\mathrm{x})$ for a system, in which a particle is in one dimensional motion, while a conservation force $F(x)$ acts on it. Suppose that $E_{\text{mech }}=8\mathrm{J}$, the incorrect statement for this system is …

A body of mass '$m$' dropped from a height '$h$' reaches the ground with a sped of $0.8\sqrt{gh}$. The value of work done by the air-friction is:

An engine is attached to a wagon through a shock absorber of length 1.5 m. The system with a total mass of $40,000\mathrm{kg}$ is moving with a speed of $72{\mathrm{kmh}}^{-1}$ when the brakes are applied to bring it to rest. In the process of the system being brought to rest, t …

A ball of mass 4 kg, moving with a velocity $10{\mathrm{ms}}^{-1}$, collides with a spring of length 8 m and force constant $100{\mathrm{Nm}}^{-1}$. The length of compressed spring is x m. The value of x, to the nearest integer, is ____

A constant power delivering machine has towed a box, which was initially at rest, along a horizontal straight line. The distance moved by the box in time '$t$' is proportional to:

As shown in the figure, a particle of mass 10 kg is placed at a point A. When the particle is slightly displaced to its right, it starts moving and reaches the point $B$. The speed of the particle at $B$ is $x\mathrm{m}/\mathrm{s}$.
(Take …

A 60 HP electric motor lifts an elevator having a maximum total load capacity of 2000 kg . If the frictional force on the elevator is 4000 N , the speed of the elevator at full load is close to: $\left(1\mathrm{HP}=746\mathrm{W},\mathrm{g}=10{\mathrm{ms}}^{-2}\right)$

A particle ( $m=1\mathrm{kg}$ ) slides down a frictionless track (AOC) starting from rest of a point A (height 2 m ). After reaching C, the particle continues to move freely in air as a projectile. When it leading its highest point P (height 1 m ) the kinetic energy of the pa …

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 $3\mathrm{m}/\mathrm{s}$. the frictional force opposing the motion is 6000 N. If the …

A particle of mass $m$ and charge $q$ is released from rest in a uniform electric field. If there is no other force on the particle, the dependence of its speed v on the distance x travelled by it is correctly given by (graphs are schematic and not drawn to scale)

An asteroid is moving directly towards the centre of the earth. When at a distance of 10 R ($R$ is the radius of the earth) from the earths centre, it has a speed of $12\mathrm{km}/\mathrm{s}$. Neglecting the effect of earths atmosphere, what will be the speed of the asteroid w …

Consider a force $\vec{F}=-x\hat{i}+y\hat{j}$. The work done by this force in moving a particle from point $A(1,0)$ to $B(0,1)$ along the line segment is: (all quantities are in SI units)

A body of mass 2 kg, is driven by an engine delivering a constant power $1\mathrm{J}/\mathrm{s}$. The body starts from rest and moves in a straight line. After 9 seconds, the body has moved a distance (in m) ____.

A cricket ball of mass 0.15 kg is thrown vertically up by a bowling machine so that it rises to a maximum height of 20 m after leaving the machine. If the part pushing the ball applies a constant force $F$ on the ball and moves horizontally a distance of 0.2 m while launching t …

Hydrogen ion and singly ionized helium atom are accelerated, from rest, through the same potential difference. The ratio of final speeds of hydrogen and helium ions is close to:

A particle is moving unidirectionally on a horizontal plane under the action of a constant power supplying energy source. The displacement(s) - time (t) graph that describes the motion of the particle is (graph are drawn schematically and are not to scale):

A particle moving in the $xy$ plane experiences a velocity dependent force $\vec{F}=k\left(v_y\hat{i}+v_x\hat{j}\right)$, where $v_x$ and $v_y$ are the $x$ and $y$ components of its velocity $\vec{v}$. If $\vec{a}$ is the acceleration of the particle, then which of the …

A solid sphere of radius R carries a charge $\mathrm{Q}+\mathrm{q}$ distributed uniformly over its volume. A very small point like piece of it of mass m gets detached from the bottom of the sphere and falls down vertically under gravity. This piece carries charge q. If it acquire …

If the potential energy between two molecules in given by $U=\frac{A}{r^6}+\frac{B}{r^{12}}$, then at equilibrium, separation between molecules, and the potential energy are:

A particle of charge $q$ and mass $m$ is subjected to an electric field $E=E_0(1-a{x}^2)$ in the x-direction, where a and $E_0$ are constants. Initially the particle was at rest at $x=0$. Other than the initial position the kinetic energy of the particle becomes zer …

A person pushes a box on a rough horizontal platform surface. He applies a force of 200 N over a distance of 15 m. Thereafter, he gets progressively tired and his applied force reduces linearly with distance to 100 N. The total distance through which the box has been moved is 30 …

A particle moves in one dimension from rest under the influence of a force that varies with the distance traveled by the particle as shown in the figure. The kinetic energy of the particle after it has traveled 3 m is:

A solid sphere and solid cylinder of identical radii approach an incline with the same linear velocity (see figure). Both roll without slipping all throughout. The two climb maximum heights $h_{\mathrm{sph}}$ and $h_{\mathrm{cyl}}$ on the incline. The radio …

A positive point charge is released from rest at a distance $r_0$ from a positive line charge with uniform density. The speed (v) of the point charge, as a function of instantaneous distance $r$ from line charge, is proportional to

A uniform cable of mass ' M ' and length ' L ' is placed on a horizontal surface such that its ${\left(\frac{1}{n}\right)}^{\text{th }}$ part is hanging below the edge of the surface. To lift the hanging part of the cable upto the surface, the work done should be:

A block of mass $m$ is kept on a platform which starts from rest with constant acceleration $\mathrm{g}/2$ upward, as shown in figure. Work done by normal reaction on block in time $t$ is:

A bullet of mass 20 g has an initial speed of $1{\mathrm{ms}}^{-1}$ just before it starts penetrating a mud wall of thickness 20 cm. If the wall offers a mean resistances of $2.5\times 10^{-2}\mathrm{N}$, the speed of the bullet after emerging from the other side of the wall i …

A force acts on a 2 kg object so that its position is given as a function of time as $\mathrm{x}=3{\mathrm{t}}^2+5$. What is the work done by this force in first 5 seconds?

A block of mass m, lying on a smooth horizontal surface, is attached to a spring (of negligible mass) of spring constant k. The other end of the spring is fixed, as shown in the figure. The block is initially at rest in a equilibrium position. If now the block is pulled with a co …

A particle is moving in a circular path of radius a under the action of an attractive potential $\mathrm{U}=-\frac{\mathrm{k}}{2{\mathrm{r}}^2}$. Its total energy is:

A body of mass $m=10^{-2}$ kg is moving in a medium and experiences a frictional force $F=-k{v}^2$. Its initial speed is $v_0=10$ ms${}^{-1}$. If, after 10 s, its energy is $\frac{1}{8}m{v}_0^2$, the value of k will be:

A time dependent force $F=6t$ acts on a particle of mass 1 kg . If the particle starts from rest, the work done by the force during the first 1 sec . will be :

A person trying to lose weight by burning fat lifts a mass of 10 kg upto a height of 1 m 1000 times. Assume that the potential energy lost each time he lowers the mass is dissipated. How much fat will he use up considering the work done only when the weight is lifted up? Fat supp …

A point particle of mass m, moves along the uniformly rough track PQR as shown in the figure. The coefficient of friction, between the particle and the rough track equals $\mu$. The particle is released, from rest, from the point P and it comes to rest at a point R. The energies, …

For a simple pendulum, a graph is plotted between its kinetic energy (KE) and potential energy (PE) against its displacement d. Which one of the following represents these correctly?
(Graphs are schematic and not drawn to scale)

When a rubber-band is stretched by a distance x, it exerts a restoring force of magnitude $\mathrm{F}=\mathrm{ax}+{\mathrm{bx}}^2$ where a and b are constants. The work done in stretching the unstretched rubber band by L is:

The potential energy function for the force between two atoms in a diatomic molecule is approximately given by $U(x)=\frac{a}{x^{12}}-\frac{b}{x^6}$, where a and b are constants and x is the distance between the atoms. If the dissociation energy of the molecule is …

A thin uniform rod of length $\ell$ and mass m is swinging freely about a horizontal axis passing through its end. Its maximum angular speed is $\omega$. Its centre of mass rises to a maximum height of

An athlete in the olympic games covers a distance of 100 m in 10 s. His kinetic energy can be estimated to be in the range

A 2 kg block slides on a horizontal floor with a speed of $4m/s$. It strikes a uncompressed spring, and compresses it till the block is motionless. The kinetic friction force is 15 N and spring constant is $10,000N/m$. The spring compresses by

A particle of mass 100 g is thrown vertically upwards with a speed of $5\text{m/s}$. The work done by the force of gravity during the time the particle goes up is