JEE Work Power Energy PYQs with Video Solutions PDF

A body of mass 2 kg is moving along x-direction such that its displacement as function of time is given by x(t) = $$\alpha t^{2} +\beta t +ym$$, where $$\alpha=1m/s^{2}, \beta=1m/s$$ and y=1m. The work done on the body during the time interval t = 2 s to t = 3 s, is _________ J.

Potential energy (V) versus distance (x) is given by the graph. Rank various regions as per the magnitudes of the force (F) acting on a particle from high lo low.

Given below are two statements:
Statement I : An object moves from position $$r_{1}$$ to position $$r_{2}$$ under a conservative force field $$\overrightarrow{F}$$.
The work done by the force is W = $$\int_{r_{1}}^{r_{2}} \overrightarrow{F}.\overrightarrow{dr}.$$
Statement II: Any object moving from one location to another location can follow infinite number of paths. Therefore, the amount of work done by the object changes with the path it follows for a conservative force.
In the light of the above statements, choose the correct answer from the options given below :

Given below are two statements:
Statement I : For a mechanical system of many particles total kinetic energy is the sum of kinetic energies of all the particles.
Statement II: The total kinetic energy can be the sum of kinetic energy of the center of mass w.r.t to the origin and the kinetic energy of all the particles w.r.t. the center of mass as the reference.
In the light of the above statements, choose the correct answer from the options given below :

Two masses m and 2m are connected by a light string going over a pulley (disc) of mass 30m with radius r = 0.1 m. The pulley is mounted in a vertical plane and it is free to rotate about its axis. The 2m mass is released from rest and its speed when it has descended through a height of 3.6 m is m/ s. (Assume string does not slip and $$g = 10m/s^{2}$$)

A small bob A of mass m is attached to a massless rigid rod of length 1 m pivoted at point P and kept at an angle of 60° with vertical as shown in figure. At distance of 1 m below point P, an identical bob B is kept at rest on a smooth horizontal surface that extends to a circular track of radius R as shown in figure. If bob B just manages to complete the circular path of radius R upto a point Q after being hit elastically by bob A, then radius R is ____ m.

An object is projected with kinetic energy K from a point A at an angle 60° with the horizontal The ratio of the difference in kinetic energies at points B and C to that at point A (see figure), in the absence of air friction is :

Two blocks with masses 100 g and 200 g are attached to the ends of springs A and B as shown in figure. the energy stored in A is E. The energy stored in B, when spring constants $$K_{A},K_{B}$$ of A and B, respectively satisfy the relation $$4K_{A}=3K_{B}$$ is:

In a perfectly inelastic collision, two spheres made of the same material with masses 15 kg and 25 kg, moving in opposite directions with speeds of 10 m/s and 30 m/s, respectively, strike each other and stick together. The rise in temperature (in $$^{\circ}C$$), if all the heat produced during the collision is retained by these spheres, is :
(specific heat of sphere material 31 cal/kg.$$^{\circ}C$$ and 1 cal =4.2 J)

Three masses 200 kg, 300 kg and 400 kg are placed at the vertices of an equilateral triangle with sides 20 m. They are rearranged on the vertices of a bigger triangle of side 25 m and with the same centre. The work done in this process ____ J. (Gravitational constant $$G=6.7 \times 10^{-11} Nm^{2}/kg^{2}$$)

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 $$30^{\circ}$$ shown in figure, the velocity at the bottom point (A) of the circular path is
(g = gravitational acceleration)

A bead $$P$$ sliding on a frictionless semi-circular string ($$ACE$$) and it is at point $$S$$ at $$t = 0$$ and at this instant the horizontal component of its velocity is $$v$$. Another bead $$Q$$ of the same mass as $$P$$ is ejected from point $$A$$ at $$t = 0$$ along the horizontal string $$AB$$, with the speed $$v$$, friction between the beads and the respective strings may be neglected in both cases. Let $$t_{P}$$ and $$t_{Q}$$ be the respective times taken by beads P and Q to reach the point B, then the relation between $$t_{P}$$ and $$t_{Q}$$ is

A block is sliding down on an inclined plane of slope 0 and at an instant t = 0 this block is given an upward momentum so that it starts moving up on the inclined surface with velocity u. The distance (S) travelled by the block before its velocity become zero, is ______.
(g = gravitational acceleration)

A ball of mass 100 g is projected with velocity 20 m/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 is 10 m/s. The ratio of its kinetic energies at point and is :

(Take acceleration due to gravity as $$10 m/s^{2}$$)

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

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 $$v_o$$ at the point ' A ', the string becomes slack when, the bob reaches at the point ' D '. The ratio of the kinetic energy of the bob at the points B and C is

________.

A ball having kinetic energy KE, is projected at an angle of $$60^{\circ}$$ from the horizontal. What will be the kinetic energy of ball at the highest point of its flight ?

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 $$\alpha=1\,N$$  then $$\beta$$ will be:

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. In the light of the above statements, choose the most appropriate answer from the options given below

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 the bead is released from top of the hoop with (negligible) zero initial speed, velocity of bead, when the length of spring becomes ' R ', would be (spring constant is 'k', g is accleration due to gravity

As shown below, bob A of a pendulum having massless string of length 'R' is released from $$60^{\circ}$$ to the vertical. It hits another bob B of half the mass that is at rest on a friction less table in the center. Assuming elastic collision, the magnitude of the velocity of bob A after the collision will be (take g as acceleration due to gravity.)

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 $$n\sqrt{gR}$$, where, $$n /geq$$, then ratio of kinetic energy of the body at bottom to that at top of the circle is

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

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A) :
Three identical spheres of same mass undergo one dimensional motion as shown in figure with initial velocities $$v_A = 5\,\text{m/s},\; v_B = 2\,\text{m/s},\; v_C = 4\,\text{m/s}$$. If we wait sufficiently long for elastic collision to happen, then $$v_A = 4\,\text{m/s},\; v_B = 2\,\text{m/s},\; v_C = 5\,\text{m/s}, will be the final velocities.
Reason (R): In an elastic collision between identical masses, two objects exchange their velocities. In the light of the above statements, choose the correct answer from the options given below :

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

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

Given below are two statements: Statement I: When speed of liquid is zero everywhere, pressure difference at any two points depends on equation $$P_1 - P_2 = \rho g(h_2 - h_1)$$. Statement II: In venturi tube shown, $$2gh = v_1^2 - v_2^2$$. Choose the most appropriate answer from the options given below.

A solid sphere and a hollow cylinder roll up without slipping on same inclined plane with same initial speed $$\upsilon$$. The sphere and the cylinder reaches upto maximum heights $$h_1$$ and $$h_2$$, respectively, above the initial level. The ratio $$h_1 : h_2$$ is $$\frac{n}{10}$$. The value of n is _____.

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

A simple pendulum of length $$1$$ m has a wooden bob of mass $$1$$ kg. It is struck by a bullet of mass $$10^{-2}$$ kg moving with a speed of $$2 \times 10^{2}$$ m s$$^{-1}$$. The bullet gets embedded into the bob. The height to which the bob rises before swinging back is. (use $$g = 10$$ m s$$^{-2}$$)

Two bodies of mass $$4$$ g and $$25$$ g are moving with equal kinetic energies. The ratio of magnitude of their linear momentum is :

The potential energy function (in J) of a particle in a region of space is given as $$U = (2x^2 + 3y^3 + 2z)$$. Here $$x, y$$ and $$z$$ are in meter. The magnitude of $$x$$-component of force (in N) acting on the particle at point $$P(1, 2, 3)$$ m is:

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, $$g = 10 \text{ m s}^{-2}$$]

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

A block of mass 1 kg is pushed up a surface inclined to horizontal at an angle of $$60°$$ 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 : $$g = 10$$ m s$$^{-2}$$

A body of mass 2 kg begins to move under the action of a time dependent force given by $$\vec{F} = (6t)\hat{i} + (6t^2)\hat{j}$$ N. The power developed by the force at the time $$t$$ is given by:

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

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 $$50 \text{ kg}$$ is lifted to a height of $$20 \text{ m}$$ 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 $$50 \text{ g}$$ is fired with a speed $$100 \text{ m/s}$$ on a plywood and emerges with $$40 \text{ m/s}$$. The percentage loss of kinetic energy is :

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

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 stationary particle breaks into two parts of masses $$m_A$$ and $$m_B$$ which move with velocities $$v_A$$ and $$v_B$$ respectively. The ratio of their kinetic energies $$(K_B : K_A)$$ is :

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

A block is simply released from the top of an inclined plane as shown in the figure above. The maximum compression in the spring when the block hits the spring is :

A particle of mass $$m$$ moves on a straight line with its velocity increasing with distance according to the equation $$v = \alpha\sqrt{x}$$, where $$\alpha$$ is a constant. The total work done by all the forces applied on the particle during its displacement from $$x = 0$$ to $$x = d$$, will be :

A heavy iron bar, of weight $$W$$ is having its one end on the ground and the other on the shoulder of a person. The bar makes an angle $$\theta$$ with the horizontal. The weight experienced by the person is :

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

A block of mass 5 kg is placed at rest on a table of rough surface. Now, if a force of 30 N is applied in the direction parallel to surface of the table, the block slides through a distance of 50 m in an interval of time 10 s. Coefficient of kinetic friction is (given, $$g = 10 \text{ m s}^{-2}$$):