JEE Exam  >  JEE Notes  >  Chapter-wise Tests for JEE Main & Advanced  >  Integer Answer Type Questions for JEE: Work, Power & Energy

Integer Answer Type Questions for JEE: Work, Power & Energy | Chapter-wise Tests for JEE Main & Advanced PDF Download

Q.1. A 100000 kg engine is moving up a slope of gradient 5° at a speed of 100 m/hr. The coefficient of friction between the engine and the rails is 0.1. If the engine has an efficiency of 4% for converting heat into work, find the amount of coal, the engine has to burn up in one hour. (Burning of 1 kg of coal yields 50000 J.)

Ans. 9154 kg
The forces are shown in Figure.
Integer Answer Type Questions for JEE: Work, Power & Energy | Chapter-wise Tests for JEE Main & Advanced

Net force to move the engine up the slope.
F = μN + mg sin θ
= mg (μ cos θ + sin θ)
If the engine has to apply an upward force equal to F,
power of engine, P = Fv
where v is the velocity equal to 100 m/hr.

Work done by engine, W = Pt  = Fvt
Efficiency of engine, η = output/Input = Fvt/Energy used
= Energy used by engine =  Fvt/η = mg(mcosq+sinq)vt/η
m = 100000 kg, μ = 0.1, θ = 5°, v = 100 m/hr, t = 1 hr
η = 4/100 = 0.04

Energy used by engine = Integer Answer Type Questions for JEE: Work, Power & Energy | Chapter-wise Tests for JEE Main & Advanced
Integer Answer Type Questions for JEE: Work, Power & Energy | Chapter-wise Tests for JEE Main & Advanced
= 4.577 x 108 J

As 1 kg coal yields 50000 J, we have the amount of coal burnt up
= Integer Answer Type Questions for JEE: Work, Power & Energy | Chapter-wise Tests for JEE Main & Advanced= 9154 kg

Q.2. Two bars of masses m1 = 4 kg and m2 = 8kg connected by a non-deformed light spring rest on a horizontal plane. The coefficient of friction between bars and surface is μ = 0.2. What minimum constant force has to be applied in the horizontal direction to the bar of mass m1 in order to shift the other bar?
Integer Answer Type Questions for JEE: Work, Power & Energy | Chapter-wise Tests for JEE Main & Advanced

Ans. 16 N

Let F be the force applied as shown in the Figure. If F moves through x, the work done will be F x x.
This is used to work against friction μm1g and store energy in the spring.
Integer Answer Type Questions for JEE: Work, Power & Energy | Chapter-wise Tests for JEE Main & Advanced
Work done against friction = μm1gx;
Energy stored = 1/2kx2 , where k is the spring constant.
∴ F × x = μm1gx + 1/2kx2... (i)
When the mass m2moves, the tension in the spring balances the force of friction at m2.
∴ kx = μm2g ... (ii)
∴ combining equations (i) and (ii),
F × x = μm1gx +1/2μm2g × x
F = Integer Answer Type Questions for JEE: Work, Power & Energy | Chapter-wise Tests for JEE Main & Advanced= 16 N

Q.3. Two masses 10 kg and 20 kg are connected by a massless spring. A force of 200 N acts on 20 kg mass. At the instant when the 10 kg mass has an acceleration 12 m/s2 the energy stored in the spring (k = 2400 N/m) will be
Integer Answer Type Questions for JEE: Work, Power & Energy | Chapter-wise Tests for JEE Main & Advanced

Ans. 3 J

F = 10 x 12 = 120 N
F = kx = 2400 x
∴ x = 1/20
Energy stored in the spring E = 1/2 kx2
Integer Answer Type Questions for JEE: Work, Power & Energy | Chapter-wise Tests for JEE Main & Advanced= 3 J

Q.4. A body is projected at an angle of 30° to the horizontal with kinetic energy 40 J. What will be the kinetic energy at the top most point?

Ans. 30 J

At the topmost point, the horizontal component of velocity = u cos α
∴ Initial kinetic energy = 1/2 mu2 = 40 J
Kinetic energy at the topmost point = 1/2 mu2 cos α
= 40 cos2α
= 40x3/4 = 30 J

Q.5. A body is slowly lowered on to a massive platform moving horizontally at a speed of 4 m/s. through what distance will the body slide relative to the platform? (The coefficient of friction is 0.2; g = 10 m/s2)

Ans. 4 m

The frictional force between the body and the platform = μmg, where m is the mass of the body.
Initially the relative velocity = 4 m/s
The relative retardation = μg

= 0.2 x 10

= 2 m/s2
If S is the relative displacement before the relative velocity becomes zero, we have
0 = 42 – 2 x 2 x S

S = 16/4 = 4 m

Q.6. A ball falls under gravity from a height 10 m with an initial velocity v0. It hits the ground, loses 50% of its energy in collision and it rises to the same height. What is the value of v0?

Ans. 14 m/s

Let v be the velocity when it hits the ground.

Then v2Integer Answer Type Questions for JEE: Work, Power & Energy | Chapter-wise Tests for JEE Main & Advanced = 2g x 10 = 2 x 9.8 x 10
i.e., v2 = Integer Answer Type Questions for JEE: Work, Power & Energy | Chapter-wise Tests for JEE Main & Advanced+ 196
Let v' be the velocity after impact and it reaches the same height 10 m.
v'2 - 0 = 2 x 9.8 x 10
v'2 = 196
v' = 14 m/s
Ratio of kinetic energy before impact and after impact
Integer Answer Type Questions for JEE: Work, Power & Energy | Chapter-wise Tests for JEE Main & Advanced
Integer Answer Type Questions for JEE: Work, Power & Energy | Chapter-wise Tests for JEE Main & Advanced= 2 x 196 – 196 = 196
v0 = 14 m/s.

Q.7. A light inextensible string that goes over a smooth fixed pulley as shown in the figure connects two blocks of masses 0.36 kg and 0.72 kg. Taking g = 10 m/s2, find the work done (in joules) by the string on the block of mass 0.36 kg during the first second after the system is released from rest.
Integer Answer Type Questions for JEE: Work, Power & Energy | Chapter-wise Tests for JEE Main & Advanced

Ans. 8 J

Given m = 0.36kg, M = 0.72kg.

The figure shows the forces on m and M.

When the system is released, let the acceleration be a. Then

Given m = 0.36kg, M = 0.72kg.

The figure shows the forces on m and M.

When the system is released, let the acceleration be a. Then
T = mg = ma

Mg − T = M
Integer Answer Type Questions for JEE: Work, Power & Energy | Chapter-wise Tests for JEE Main & Advanced
∴ Work done by the string on m is
Integer Answer Type Questions for JEE: Work, Power & Energy | Chapter-wise Tests for JEE Main & Advanced

Q.8. Three objects A, B and C are kept in a straight line on a frictionless horizontal surface. These have masses m, 2m and m, respectively. The object A moves towards B with a speed 9 m/s and makes an elastic collision with it. There after, B makes completely inelastic collision with C. All motions occur on the same straight line. Find the final speed (in m/s) of the object C.
Integer Answer Type Questions for JEE: Work, Power & Energy | Chapter-wise Tests for JEE Main & Advanced

Ans. 4m/s

The velocity of B just after collision with A is
Integer Answer Type Questions for JEE: Work, Power & Energy | Chapter-wise Tests for JEE Main & Advanced
Integer Answer Type Questions for JEE: Work, Power & Energy | Chapter-wise Tests for JEE Main & Advanced
The collision between B and C is completely inelastic.
∴ mB vB = (mB +mc)v

Integer Answer Type Questions for JEE: Work, Power & Energy | Chapter-wise Tests for JEE Main & Advanced

Q.9. A block of mass 0.18 kg is attached to a spring of force-constant 2 N/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 0.06 m and comes to rest for the first time. The initial velocity of the  block in m/s is V = N/10. Then N is
Integer Answer Type Questions for JEE: Work, Power & Energy | Chapter-wise Tests for JEE Main & Advanced

Ans. 4

Let v be the speed of the block just after impulse. At B, the block comes to rest. Therefore
Integer Answer Type Questions for JEE: Work, Power & Energy | Chapter-wise Tests for JEE Main & Advanced 
Loss in K.E. of the block = Gain in RE. of the spring + Work done against friction
Integer Answer Type Questions for JEE: Work, Power & Energy | Chapter-wise Tests for JEE Main & Advanced
∴ v = 4/10  ∴ N = 4

Q.10. A particle of mass 0.2 kg is moving in one dimension under a force that delivers a constant power 0.5 W to the particle. If the initial speed (in ms-1) of the particle is zero, the speed (in ms-1) after 5 s is

Ans. 5ms-1

Here Δ K.E. = W = p x t
∴ 1/2 mv2 = P x t
Integer Answer Type Questions for JEE: Work, Power & Energy | Chapter-wise Tests for JEE Main & Advanced

The document Integer Answer Type Questions for JEE: Work, Power & Energy | Chapter-wise Tests for JEE Main & Advanced is a part of the JEE Course Chapter-wise Tests for JEE Main & Advanced.
All you need of JEE at this link: JEE
446 docs|930 tests

Top Courses for JEE

446 docs|930 tests
Download as PDF
Explore Courses for JEE exam

Top Courses for JEE

Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev
Related Searches

video lectures

,

Power & Energy | Chapter-wise Tests for JEE Main & Advanced

,

Previous Year Questions with Solutions

,

Important questions

,

shortcuts and tricks

,

Integer Answer Type Questions for JEE: Work

,

Power & Energy | Chapter-wise Tests for JEE Main & Advanced

,

Objective type Questions

,

practice quizzes

,

Power & Energy | Chapter-wise Tests for JEE Main & Advanced

,

Integer Answer Type Questions for JEE: Work

,

Exam

,

Extra Questions

,

pdf

,

ppt

,

mock tests for examination

,

Summary

,

MCQs

,

study material

,

Free

,

Semester Notes

,

Sample Paper

,

Integer Answer Type Questions for JEE: Work

,

past year papers

,

Viva Questions

;