Work, Power & Energy — JEE Main PYQs

Given below are two statements:
Statement I: An object moves from position $r_1$ to position $r_2$ under a conservative force field $\vec{F}$. The work done by the force is $W=-{\int }_{r_1}^{r_2}\vec{F}\cdot \overrightarrow{dr}$.
Statement II: Any object moving from one l …

Consider two identical metallic spheres of radius $R$ each having charge $Q$ and mass $m$. Their centers have an initial separation of $4R$. Both the spheres are given an initial speed of $u$ towards each other. The minimum value of $u$, so that they can just touch e …

A body of mass 2 kg is moving along x-direction such that its displacement as function of time is given by $\mathrm{x}(\mathrm{t})=\alpha {\mathrm{t}}^2+\beta \mathrm{t}+\gamma \mathrm{m}$, where $\alpha =1\mathrm{m}/{\mathrm{s}}^2$, $\beta =1\mathrm{m}/\mathrm{s}$ an …

In case of vertical circular motion of a particle by a thread of length r if the tension in the thread is zero at an angle 30° shown in figure, the velocity at the bottom point (A) of the circular path is (g = gravitational acceleration)

A spherical ball of mass 2 kg falls from a height of 10 m and is brought to rest after penetrating 10 cm into sand. The average force exerted by sand on the ball is $\_\_\_\_$ N.

A 1 kg block subjected to two simultaneous forces $(2\hat{i}+3\hat{j}+4\hat{k})$ N and $(3\hat{i}-\hat{j}-2\hat{k})$ N is moved a distance of 25 m along $(3\hat{i}-4\hat{j})$ direction. The work done in this process is _____ J.

A body of mass 2 kg begins to move under the influence of time dependent force $\vec{F}=(2t\hat{i}+6t^2\hat{j})$ N, where $\hat{i}$ and $\hat{j}$ are unit vectors along x and y-axis respectively. The power produced by the force at $t=2$ s is _____ W.

A mass of 1 kg kept in a inclined plane with $30^{\circ }$ inclination with respect to horizontal plane and it is at rest initially. Then the whole assembly is moved up with constant velocity of $4\text{m/s}$. The work done by the frictional force in time 2 s is ______ J.
(T …

The rain drop of mass 1 g, starts with zero velocity from a height of 1 km. It hits the ground with a speed of $5\mathrm{m}/\mathrm{s}$. The work done by the unknown resistive force is ______ J. (take $\mathrm{g}=10\mathrm{m}/{\mathrm{s}}^2$)

A smooth inclined plane ends in a vertical circular loop, as shown in the figure. A small body is released from height $h$ as shown. If the body exerts a force of three times its weight on the plane at the highest point of circle then the height $h=\alpha \mathrm{R}$. The val …

A body of mass 1 kg moves along a straight line with a velocity $v=2x^2$. The work done by the body during displacement from $x=0$ to 5 m is ______ J.

The velocity at which 6 kg mass (shown in figure) strikes the ground when it is released from a height of 6 m above the ground is ______ $\mathrm{m}/\mathrm{s}$. Assume pulley is massless and string is light and inextensible (Take $\mathrm{g}=10\mathrm{m}/{\mathrm{s}}^2$).

A bob of mass m is suspended at a point O by a light string of length $l$ and left to perform vertical motion (circular) as shown in figure. Initially, by applying horizontal velocity $v_0$ at the point 'A', the string becomes slack when the bob reaches at the point 'D'. The ra …

A force $\vec{F}=2\hat{i}+b\hat{j}+\hat{k}$ is applied on a particle and it undergoes a displacement $\hat{i}-2\hat{j}-\hat{k}$. What will be the value of $b$, if work done on the particle is zero.

A ball of mass 100 g is projected with velocity $20\mathrm{m}/\mathrm{s}$ at $60^{\circ }$ with horizontal. The decrease in kinetic energy of the ball during the motion from point of projection to highest point is :

A body of mass 100 g is moving in circular path of radius 2 m on vertical plane as shown in figure. The velocity of the body at point A is $10\mathrm{m}/\mathrm{s}$. The ratio of its kinetic energies at point B and C is :
(Take acceleration due to gravity as …

A solid sphere of mass ' $m$ ' and radius ' $r$ ' is allowed to roll without slipping from the highest point of an inclined plane of length 'L' and makes an angle $30^{\circ }$ with the horizontal. The speed of the particle at the bottom of the plane is ${\mathrm{v}}_1$. If the an …

A force $\mathrm{f}={\mathrm{x}}^2\mathrm{y}\hat{\mathrm{i}}+{\mathrm{y}}^2\hat{\mathrm{j}}$ acts on a particle in a plane $\mathrm{x}+\mathrm{y}=10$. The work done by this force during a displacement from $(0,0)$ to $(4\mathrm{m},2\mathrm{m})$ is $\_\_\_\_$ Joule (round …

A sand dropper drops sand of mass $\mathrm{m}(\mathrm{t})$ on a conveyer belt at a rate proportional to the square root of speed $(\mathrm{v})$ of the belt, i.e. $\frac{\mathrm{dm}}{\mathrm{dt}}\propto \sqrt{\mathrm{v}}$. If P is the power delivered to run the belt at constant s …

A body of mass ' $m$ ' connected to a massless and unstretchable string goes in verticle circle of radius ' R ' under gravity g . The other end of the string is fixed at the center of circle. If velocity at top of circular path is $\mathrm{n}\sqrt{\mathrm{gR}}$, where, …

A body of mass 4 kg is placed on a plane at a point P having coordinate $(3,4)\mathrm{m}$. Under the action of force $\overrightarrow{\mathrm{F}}=(2\hat{\mathrm{i}}+3\hat{\mathrm{j}})\mathrm{N}$, it moves to a new point Q having coordinates $(6,10)\mathrm{m}$ in 4 sec . The …

A bead of mass '$m$' slides without friction on the wall of a vertical circular hoop of radius 'R' as shown in figure. The bead moves under the combined action of gravity and a massless spring (k) attached to the bottom of the hoop. The equilibrium length of the spring is 'R'. If …

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A: In a central force field, the work done is independent of the path chosen
Reason R: Every force encountered in mechanics does not have an associated potential energy. …

A particle of mass ' $m$ ' and charge ' $q$ ' is fastened to one end 'A' of a massless string having equilibrium length $\ell$, whose other end is fixed at point ' $O$ '. The whole system is placed on a frictionless horizontal plane and is initially at rest. If uniform electric f …

A force $F=\alpha +\beta x^2$ acts on an object in the x -direction. The work done by the force is 5 J when the object is displaced by 1 m . If the constant $\alpha =1\mathrm{N}$ then $\beta$ will be

A particle is released from height S above the surface of the earth. At certain height its kinetic energy is three times its potential energy. The height from the surface of the earth and the speed of the particle at that instant are respectively.

Two cylindrical vessels of equal cross sectional area of $2{\mathrm{m}}^2$ contain water upto height 10 m and 6 m, respectively. If the vessels are connected at their bottom then the work done by the force of gravity is : (Density of water is …

A block of mass 1 kg, moving along x with speed $v_i=10\text{m/s}$ enters a rough region ranging from $x=0.1\text{m}$ to $x=1.9\text{m}$. The retarding force acting on the block in this range is $F_r=-kx\text{N}$, with $k=10\text{N/m}$. Then the final spee …

Which one of the following forces cannot be expressed in terms of potential energy?

An object of mass 1000 g experiences a time dependent force $\vec{F}=(2t\hat{i}+3t^2\hat{j})$ N. The power generated by the force at time $t$ is:

A block of mass 2 kg is attached to one end of a massless spring whose other end is fixed at a wall. The spring-mass system moves on a frictionless horizontal table. The spring's natural length is 2 m and spring constant is $200\mathrm{N}/\mathrm{m}$. The block is pushed such …

When kinetic energy of a body becomes 36 times of its original value, the percentage increase in the momentum of the body will be :

A body of m kg slides from rest along the curve of vertical circle from point $A$ to $B$ in friction less path. The velocity of the body at B is :

(given, $\mathrm{R}=14\mathrm{m},\mathrm{g}=10\mathrm{m}/{\mathrm{s}}^2$ and $\sqrt{2}=1.4$ )

If a rubber ball falls from a height h and rebounds upto the height of $\mathrm{h}/2$. The percentage loss of total energy of the initial system as well as velocity ball before it strikes the ground, respectively, are :

A body is moving unidirectionally under the influence of a constant power source. Its displacement in time t is proportional to :

A body of mass 50 kg is lifted to a height of 20 m from the ground in the two different ways as shown in the figures. The ratio of work done against the gravity in both the respective cases, will be:

A bullet of mass 50 g is fired with a speed $100\mathrm{m}/\mathrm{s}$ on a plywood and emerges with $40\mathrm{m}/\mathrm{s}$. The percentage loss of kinetic energy is :

Four particles $\mathrm{A},\mathrm{B},\mathrm{C},\mathrm{D}$ of mass $\frac{\mathrm{m}}{2},\mathrm{m},2\mathrm{m},4\mathrm{m}$, have same momentum, respectively. The particle with maximum kinetic energy is :

Three bodies A, B and C have equal kinetic energies and their masses are $400\mathrm{g},1.2\mathrm{kg}$ and 1.6 kg respectively. The ratio of their linear momenta is :

A particle of mass $m$ moves on a straight line with its velocity increasing with distance according to the equation $\mathrm{v}=\alpha \sqrt{\mathrm{x}}$, where $\alpha$ is a constant. The total work done by all the forces applied on the particle during its displacement from …

A force $\left(3x^2+2x-5\right)N$ displaces a body from $\mathrm{x}=2\mathrm{m}$ to $\mathrm{x}=4\mathrm{m}$. Work done by this force is ...........J.

A ball suspended by a thread swings in a vertical plane so that its magnitude of acceleration in the extreme position and lowest position are equal. The angle ($\theta$) of thread deflection in the extreme position will be :

The bob of a pendulum was released from a horizontal position. The length of the pendulum is 10 m. If it dissipates $10\%$ of its initial energy against air resistance, the speed with which the bob arrives at the lowest point is: [Use, $g:10$ ms${}^{-2}$]

A bob of mass 'm' is suspended by a light string of length 'L'. It is imparted a minimum horizontal velocity at the lowest point A such that it just completes half circle reaching the top most position B. The ratio of kinetic energies …

The potential energy function (in J) of a particle in a region of space is given as $\mathrm{U}=\left(2{\mathrm{x}}^2+3{\mathrm{y}}^3+2\mathrm{z}\right)$. Here x, y and z are in meter. The magnitude of x-component of force (in N) acting on the particle at point …

A block of mass 100 kg slides over a distance of 10 m on a horizontal surface. If the co-efficient of friction between the surfaces is 0.4, then the work done against friction (in J) is:

A solid circular disc of mass 50 kg rolls along a horizontal floor so that its center of mass has a speed of $0.4\mathrm{m}/\mathrm{s}$. The absolute value of work done on the disc to stop it is ______ J.

A disc of radius R and mass M is rolling horizontally without slipping with speed $\nu$. It then moves up an inclined smooth surface as shown in figure. The maximum height that the disc can go up the incline is :

A block of mass 1 kg is pushed up a surface inclined to horizontal at an angle of $60^{\circ }$ by a force of 10 N parallel to the inclined surface as shown in figure. When the block is pushed up by 10 m along inclined surface, the work done against frictional force is: …

A particle is placed at the point A of a frictionless track ABC as shown in figure. It is gently pushed toward right. The speed of the particle when it reaches the point $B$ is : (Take $g=10\mathrm{m}/{\mathrm{s}}^2$ ).