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JEE Main Test Series - Work, Energy and Power, Sample Questions with Solutions

A significant chapter in JEE is Work, Power, and Energy. Solving the question papers from previous years allows students to examine the pattern of questions and to understand the study process. The weightage of the chapter is 1 question of 4 marks in JEE Main Question Papers

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Here, from the chapter Work, Energy, and Power, you will be presented with 10 solved practice questions for JEE Main 2021. This test includes work done by a theorem of Work, kinetic energy, potential energy, and work-energy. 

  • When there is a motion of the object with the application of external force, work is done. Work is determined to be the product of force and the object's displacement. For example, 100 joules (J) of work can be performed by a force of 20 newtons (N) moving an object 5 meters in the same direction of power. 
  • Energy is characterized, in simple words, as the capacity to do work. Energy is converted and it can not be destroyed from one form to another. Energy is present in various ways, such as mechanical energy, electricity, kinetic energy, potential energy, and many more. 
  • Generally speaking, power is characterized as the rate of doing work. That is the amount of energy per unit of time that is consumed. 

MCQs with 1 Answer

JEE Main- Multiple choice questions with one correct Answer

  1. Two masses of 1 g and 4g are moving with equal kinetic energy. The ratio of the magnitudes of their momenta is [1980-2 marks]
    1. 4:1
    2. √2:1
    3. 1:2
    4. 1:16

Ans. 

Ques 1
  1. If a machine is lubricated with oil. [1980-2 marks]
    1. the mechanical advantage of the machine increases
    2. the mechanical efficiency of the machine increases
    3. both its mechanical advantage and efficiency increase
    4. its efficiency increases, but its mechanical advantage decreases.

Ans. 

(b) When a machine is lubricated with oil friction decreases. Hence the mechanical efficiency of the machine increases.

  1. A particle of mass m is moving in a circular path of constant radius r such that its centripetal acceleration ac is varying with time ‘t’ as ac = k2rt2where ‘k’ is a constant. The power delivered to the particle by the force acting on it is [1994-1 mark]
    1. 2πmk2r2t
    2. mk2r2t
    3. (mk4r2t5)/3
    4. Zero

Ans. 

Ques 3
  1. A stone tied to a string of length L is whirled in a vertical circle with the other end of the string at the center. At a certain instant of time, the stone is at its lowest position and has a speed u. The magnitude of the change in its velocity as it reaches a position where the string is horizontal is [1998-2 marks]
    1. u2-2gl
    2. 2gl
    3. u2-gl
    4. 2 (u2-gl)

Ans. 

Ques 4
  1. A spring of force constant k is cut into two pieces such that one piece is double the length of the other. Then the long piece will have a force constant of [1999-2 marks]
    1. (⅔)k 
    2. (3/2)k 
    3. 3k
    4. 6k

Ans. 

Ques 5
  1. A wind-powered generator converts wind energy into electrical energy. Assume that the generator converts a fixed fraction of the wind energy intercepted by its blades into electrical energy. For wind speed v, the electrical power output will be proportional [2000]
    1. v
    2. v2
    3. v3
    4. v4

Ans.

Ques 6
  1. A particle, which is constrained to move along the x-axis, is subjected to a force in the same direction which varies with the distance x of the particle from the origin as F (x) = -kx + ax3. Here k and a are positive constants. For x>0, the functional graphically form of the potential energy U(x)of the particle is [2000]
Ques 7

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Ans 7
  1. An ideal spring with spring constant k is hung from the ceiling and a block of mass M is attached to its lower end. The mass is released with the spring initially unstretched. Then the maximum extension in the spring is [2002]
Ques 8

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Ans 8
Ques 8
  1. If W1, W2, and W3 represent the work done in moving a particle from A to B along three different, paths 1,2 and 3 respectively (as shown) in the gravitational field of a point mass m, find the correct relation between W1, W2 and W3 [2003]
Ques 9
  1. W1>W2>W3
  2. W1 = W2 = W3
  3. W1 < W2 < W3
  4. W2 >W1 >W3

Ans.

(b) The gravitational field is a conservative field. In a conservative field, the work done W does not depend on the path (from A to B). It depends on the initial and final points W1=W2 = W3

  1. A particle is acted by a force F=kx, where k is a +ve constant. Its potential energy at x=0 is zero. Which curve correctly represents the variation of the potential energy of the block with respect to x? [2004]
Ques 10

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Ans 10
  1. A Bob of mass M is suspended by a massless string of length L. the horizontal velocity V at position A is just sufficient to make it reach the point B. the angle Ө at which the speed of the bob is half of the A, satisfies [2008]
Ques 11

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Ans 11
  1. A block of mass 2 kg is free to move along the x-axis. It is at rest and from t = 0 onwards it is subjected to a time-dependent force F(t) in the x-direction. The force F(t) varies with t as shown in the figure. The kinetic energy of the block after 4.5 seconds is
Ques 12
  1. 4.50 J
  2. 7.50 J
  3. 5.06 J
  4. 14.06 J

Ans.

Ans 12

MCQs with more than 1 Answer

JEE Main - Multiple choice questions with more than one correct answers

  1. A uniform chain of length L and mass M is lying on a smooth table and one-third of its length is hanging vertically down over the edge of the table. If g is the acceleration due to gravity, the work required to pull the hanging part on to the table is [1985-2 marks]
    1. Mgl
    2. Mgl/3 
    3. Mgl/9
    4. Mgl/18

Ans. 

Ans 13
  1. A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle. The motion of the particle takes place in a plane. It follows that [1987-2 marks]
    1. its velocity is constant
    2. its acceleration is constant
    3. its kinetic energy is constant
    4. it moves in a circular path

Ans. 

(c), (d) It is a case of uniform circular motion. Ve­locity and acceleration keep on changing their di­rections. Their magnitudes remain constant. Kinetic energy remains constant.Options (c) and (d) are correct.

  1. A small ball starts moving from A over a fixed track as shown in the figure. Surface AB has friction. From A to B the ball rolls without slipping. Surface BC is frictionless. KA, KB, and Kc are kinetic energies of the ball at A, B, and C respectively. Then [2006-5 marks]
Ques 15
  1. hA > hc;KB > Kc
  2.  hA > hc;KB > Kc
  3. hA = hc;KB = Kc
  4. hA < hc;KB > Kc
Ans 15

CBQs with Solutions

JEE Main - Comprehension Based Questions with Solutions

  1. A small block of mass M moves on a frictionless surface of an inclined plane, as shown in the figure. The angle of the incline suddenly changes from 60° to 30° at point B. The block is initially at rest at A. Assume that collisions between the block and the incline are totally inelastic (g=10 m/s2)
Ques 16
  1. The speed of the block at point B immediately after it strikes the second incline is
    1. 60m/s
    2. 45m/s
    3. 55m/s
    4. 15m/s

Ans.

Ans 17
  1. The speed of the block at point C, immediately before it leaves the second incline is
    1. 120m/s
    2. 105m/s
    3. 90m/s
    4. 75m/s

Ans.

Ans 18
  1. If the collision between the block and the incline is completely elastic, then the vertical (upward) component of the velocity of the block at point B, immediately after it strikes the second incline is
    1. 30m/s
    2. 15m/s
    3. 0
    4. -15m/s

Ans.

(c) The velocity of the block coming down from the incline AB makes an angle 30° with the incline BC. If the block collides with the incline BC elastically, the angle of the velocity of the block after collision with the incline shall be 30°. Hence just after collision with the incline BC, the velocity of a block shall be horizontal. So immediately after the clock strikes the second incline, its vertical component of velocity will be zero.

  1. The displacement x of a particle moving in the one dimension, under the action of a constant force is related to the time t by the equation t=x+3 where x is in meter and t in second. Find [1980]
    1. The displacement of the particle when it’s velocity is zero, and 
    2. The work done by the force in the first 6 seconds.

Ans.

Ans 20
  1. A pulley arrangement is shown in the figure. Cylinder A has a dia­meter of 30cm and cylinder B has a dia­meter of 20cm. The working handle has an arm of 50cm. The direction of winding of the rope on A is opposite to that on B. Calculate the mechanical advantage of this arrangement. [1980]
Ques 21

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Ans 21
Ans 21
  1. A body of mass 2kg is being dragged with a uniform velocity of 2m/s on a rough horizontal plane. The coefficient of friction between the body and the surface is 0.20, J=4.2 joule/calorie, and g = 9.8m/s2. Calculate the amount of heat generated in 5 seconds. [1980-5 marks]

Ans.

Ans 22
  1. In the figures (a) and (b), AC, DG and GF are fixed inclined planes, BC = EF = x and AB = DE = y. A small block of mass is released from point A. It slides down AC and reaches C with a speed vc. The same block is released, from rest, from point D. It slides down DGF and reaches point F with speed vF. The coefficients of kinetic frictions, between the block and both the surfaces AC and DGF, are u Calculate vc and vF. [1980-6 marks]
Ques 23
Ans 23

Ans.

  1. A lead bullet just melts when stopped by an obstacle. Assuming that 25 percent of the heat is absorbed by the obstacle, find the velocity of the bullet. Its initial temperature is 27°C.(Melting point of lead = 327° C, specific heat of lead = 0.03 calorie/g°C, latent heat of fusion of lead = 6 cal/g° C, J = 4.2 joule/calorie).[1981-3 marks]
Ques 24

Ans.

  1. Two blocks A and B are connected to each other by a string and a spring; the string passes over a frictionless pulley as shown in the figure. Block B slides over the horizontal top surface of a stationary block C and blocks A slides along the vertical side of C, both with the same uniform speed.
Ques 25

The coefficient of friction between the surfaces of blocks is 0.2. The Force constant of the spring is 1960 newton/m. If the mass of block A is 2kg, calculate the mass of block B and the energy stored in the spring. [1982-5 marks]

Ans. 

Both A and B are moving with uniform speed. Their acceleration is zero and so the force on them should be zero. The spring is loaded. Let the ex­tension of the spring be x. The force acting on the spring is the tension T. The tension T is set up in the string. Free body diagrams of B, spring, and A are shown in the figures.

Ans 26
  1. A 0.5 kg block slides from point A ( see fig) on a horizontal track with an initial speed of 3 m/s towards a weightless horizontal spring of length 1 m and forces constant 2 newton/m. The part AB of the track is frictionless and the part BC has the co­efficients of static and kinetic friction as 0.22 and 0.2 respectively. If the distances AB and BD are 2 m and 2.14 m respectively, find the total distance through which the block moves before it comes to rest completely. (Take g = 10 m/s2).[1983-7 marks]
Ques 26

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Ans 26
Ans 26

Part AB of the track is frictionless. Hence no energy is lost along with AB. The 0.5 kg block travels to the spring and compresses the spring by an amount x. Energy is stored in the spring. The kinetic energy of block = Work done against kinetic friction + po­tential energy of spring

  1. A string, with one end fixed on a rigid wall, passing over a fixed frictionless pulley at a distance of 2 m from the wall, has a point mass M = 2 kg attached to it at a distance of 1 m from the wall. A mass m = 0.5 kg attached at the free end is held at rest so that the string is horizontal between the wall and the pulley and vertical beyond the pulley. What will be the speed with which the mass M will hit the wall when the mass m is released? [1985-6 marks]
Ques 27

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Ans 27
Ans 27
  1. A block of mass 0.18 kg is attached to a spring of force-constant 2N/m. The coefficient of friction between the block and the floor is 0.1. Initially, the block is at rest and the spring is un-stretched. An impulse is given to the block as shown in the figure. The block slides a distance of 0.06m and comes to rest for the first time. The initial velocity of the block in m/s is V = N/10. Then N is [2011]
Ques 28

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Ans 28

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