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All questions of Work, Energy & Power for JAMB Exam

 For what angle between Force and Displacement will the work done be positive?
  • a)
  • b)
  • c)
  • d)
Correct answer is option 'C'. Can you explain this answer?

Om Desai answered
  • If a force acting on a body has a component in the opposite direction of displacement, the work done is negative.
  • So when a body slides against a rough horizontal surface, its displacement is opposite to that of the force of friction. The work done by the friction is negative.

Work done by gravitational force on a man, in lifting a bucket out of the well by rope tied to the bucket is
  • a)
    negative
  • b)
    positive
  • c)
    zero
  • d)
    infinity
Correct answer is option 'A'. Can you explain this answer?

Om Desai answered
When the man pulls the bucket outside the well the gravitational potential of the man + bucket system increases and hence the work done by the gravitational force is negative.

An engine generates a power of 10 kW. In how much time will it raise a mass of 200 kg through a height of 40m.
  • a)
    4 sec
  • b)
    10 sec
  • c)
    5 sec
  • d)
    8 sec
Correct answer is option 'D'. Can you explain this answer?

Mira Sharma answered
Power = work done / time 


work = force x distance 


so power = (force x distance) / time 


time = (force x distance) / power 


= (2000 N x 40m) / 10000W = 8 seconds

A body dropped from height H reaches the ground with a speed of showimage (1)
  • a)
    mgh
  • b)
    -0.28mgH
  • c)
    2gh
  • d)
    0.5gh
Correct answer is option 'B'. Can you explain this answer?

Krishna Iyer answered
The forces acting on the body are the force of gravity and the air friction. By work energy theorem, the total work done on the body is
W=1/2m(1.2√gH)2−0=0.72mgH
The work done by the force of gravity is mgH.
. Hence, the work done by the air friction is,
=0.72mgH-mgH
=00.28mgH.
 

A person 'A' pushes a body of 5 kg placed on a rough surface of co-efficient of friction 0.3 by a distance of 4 m in 15 seconds. Another person 'B' pushes the body of 7 kg on same surface by a distance of 3 m in the same time. Who has more energy and power?
  • a)
    A
  • b)
    B
  • c)
    Both A and B have developed equal power but B has more energy
  • d)
    Both A and B have developed equal power but A has more energy
Correct answer is option 'B'. Can you explain this answer?

Gaurav Kumar answered
For person A,
Mass of body, m= 5kg
Coefficient of friction, μ =0.3
So, The force of friction,
F1= μm1g=0.3 X 5 X 10=15N
Displacement, S1=4m
Therefore,
Work done, W1=15X4=60J
Time taken, t1=15sec
So, Power, P1=60/15=4W
For Person B
Mass of body, m2=7kg
Coefficient of friction, μ =0.3
So, The force of friction,
F1= μm2g=0.3 X 7 X 10=21N
Displacement, S2=3m
Therefore,
Work done, W2=21X3=63J
Time taken, t2=15sec
So, Power, P3=63/15=4.2W
So person B has more energy and power.

 A man A of mass 80 kg runs up a staircase in 12 seconds. Another man of mass 60 kg runs up the same staircase in 11 seconds. The ratio of powers of A and B is :
  • a)
    11:12
  • b)
    9:11
  • c)
    12:11
  • d)
    11:9
Correct answer is option 'D'. Can you explain this answer?

Naina Sharma answered
According to question, 60 kg man runs up a staircase in 12 sec.
m₁ = 80 kg
t₁ = 12 sec
=> A 50 kg man runs up the same staircase in 11 sec:
m₂ = 60 kg
t₂ = 11 sec
=> Rate of work done is equals to power.
∴ P = E/ t and E = mgh
∴ P₁ = m₁gh / t₁
P₂ = m₂gh/ t₂
=> The ratio of Power or Rate of work done is:
P₁/P₂ = m₁gh / t₁ / m₂gh/ t₂
= m₁ * t₂ / m₂ * t₁
= 80x11/60x12
= 11 : 9
Thus, the ratio of rate of doing their work is 11 : 9.

Time rate at which work is done by a force is
  • a)
    Power
  • b)
    Torque
  • c)
    Centrifugal Force
  • d)
    Acceleration
Correct answer is option 'A'. Can you explain this answer?

Gaurav Kumar answered
We know that Work done, W = F.s
where F is force and s is displacement due to that force.
Thus rate of work done is: 
dW/dt = d(F.s)/dt
So as F is constant we get, 
dW/dt = F.d(s)/dt = F.v = P (Power)

By how much does kinetic energy increase if the momentum is increased by 20%?
  • a)
    55 %
  • b)
    20 %
  • c)
    44 %
  • d)
    60 %
Correct answer is option 'C'. Can you explain this answer?

Hansa Sharma answered
The kinetic energy is given by: 
KE= p2/2m
So, ΔKE = 2pΔp​ / 2m = pΔp / m​
ΔKE / KE ​= (pΔp/m)​ * (2m/p2)​ = 2Δp / p
Since the momentum p increases by 20%, so the final momentum becomes 1.2p.
Hence, KEfinal​ = (1.2p)/ 2m​ = 1.44p2 / 2m​ = 1.44KE
So, % change in KE = 44%

There are two bodies X and Y with equal kinetic energy but different masses m and 4m respectively. The ratio of their linear momentum is-
  • a)
    1:2
  • b)
    4:1
  • c)
    1:√2
  • d)
    1:4
Correct answer is option 'A'. Can you explain this answer?

Suresh Iyer answered
X and Y have equal kinetic energy but their masses are m and 4m respectively.
► 1/2 m1v12 = 1/2 m2v22  
► mv12 = 4m * v22  
► v1 : v2 = 2 : 1
Hence the ratio of their linear momentum is:
m1v1 : m2v2 = m * 2v : 4m * v = 1 : 2

A wheel is at rest. Its angular velocity increases uniformly and becomes 80 radian per second after 5 second. The total angular displacement is :
  • a)
    800 Red
  • b)
    400 Red
  • c)
    200 Red
  • d)
    100 Red
Correct answer is option 'C'. Can you explain this answer?

As stated

if the angular velocity increases uniformly . The angular acceleration must be constant.

Hence the formula

s= ut+ 0.5 a t^2

Where.

u= initial angular velocity

a= angular acceleration (i.e = 80/5=16 rad/s^2)

S= angular displacement

t= time taken

Now.

s= 0 + 0.5 X 16*5*5 = 200

Hence angar displacement = 200 radians

 A body moves under a force such that momentum of the body at any instant showimage (3). What is the rate of work done by the force?
  • a)
  • b)
  • c)
  • d)
    zero
Correct answer is option 'D'. Can you explain this answer?

Hansa Sharma answered
P = p Cos(t) i + p Sin(t) j
dP/dt = -p Sin(t) j + p Cos(t) i
Work done, W = P2/2m
Rate of work done = d/dt(P2/2m)
= 2P/2m x dP/dt
= P/m x dP/dt
= -p2.Sin(t).Cos(t) + p2.Sin(t).Cos(t)
=> Rate of work done = 0

How much work is done by a man weighing 80 kgf in raising a stone of weight 20 kgf to the top of a building of height 40 m? (g = 9.8 m/s2)
  • a)
    30,900 J
  • b)
    29,678 J
  • c)
    39,200 J
  • d)
    25,000 J
Correct answer is option 'C'. Can you explain this answer?

Sushil Kumar answered
Total mass=80+20=100
w=mgh(where m=100, g=9.8, h=40m)
w=100×9.8×40
w=39200J
work done by man weighing 80 kg raising a stone of 20kgf to the top of building of Height is 40m is 39,200J

An elastic spring of force constant k is compressed by an amount x. Then its potential energy will be
  • a)
    kx
  • b)
    -kx
  • c)
  • d)
Correct answer is option 'D'. Can you explain this answer?

Anjana Sharma answered
F= kx 

Now as we know 

f.ds = potential energy 

differentiate 
 
potential energy = kx .ds 

k is a constant .... and diff of x .ds is = x^2 / 2 


so here potential energy will be = 1/2 k x^2

How should the force applied on a body be varied with velocity to keep the power of force constant?
  • a)
    Force should be inversely proportional to the square root of the velocity of the body
  • b)
    Force should be inversely proportional to the velocity of the body
  • c)
    Force should be directly proportional to the velocity of the body
  • d)
    Force should not be varied. It should remain constant with the velocity
Correct answer is option 'B'. Can you explain this answer?

Anjana Sharma answered
We know that power (P) = force (F) x velocity (v).
Since the body is moving with acceleration,v changes and as a result of that P also changes,F being constant.
For P to be constant, F v = constant or F ∝ 1/v i.e 
Force should be inversely proportional to the velocity of the body.

Thus,as v increases, F should decrease to keep P constant. 

 In the given figure, what is the work done by the spring force?
  • a)
  • b)
  • c)
  • d)
Correct answer is option 'C'. Can you explain this answer?

Neha Joshi answered
We know that for a spring with spring constant k, work done by the spring when a compression or expansion is done of some length say x is ½ kx2
Also as the work done is in the opposite direction to that of force applied, we get the sign of the force to be negative.

 A machine gun fires 60 bullets per minute, with a velocity of 700 m/s. If each bullet has a mass of 50g, find the power developed by the gun.
  • a)
    1225 W
  • b)
    12250 W
  • c)
    122.5 W
  • d)
    122 W
Correct answer is option 'B'. Can you explain this answer?

Tejas Verma answered
Each bullet will have KE = 1/2 * 0.05 * 700 * 700 = 12250 J
So for 60 bullets the energy given by machine in 60 second = 60 x 12250 J
Hence power developed = Energy / time =60 x12250/60 =12250W
Or power = 12.250 kW.

Which of the following is not conserved in inelastic collision?
  • a)
    momentum
  • b)
    kinetic energy
  • c)
    both momentum and kinetic energy
  • d)
    neither momentum nor kinetic energ
Correct answer is option 'B'. Can you explain this answer?

Rajesh Gupta answered
In an inelastic collision, the force of reformation is not equal to the force of deformation and thus some amount of energy is lost. But still as no external force acts upon the system momentum is still conserved.

Which of the following statement is not related to conservative force?
  • a)
    Work done in closed path is zero
  • b)
    Work done is recoverable
  • c)
    Path independent
  • d)
    Path dependent
Correct answer is option 'D'. Can you explain this answer?

Krishna Iyer answered
A force is said to be conservative if the work done by or against the force on a body is independent of path followed by the body and depends only on initial and final positions.
Work done by or against the conservative force in moving a particle along a closed path is zero.

Which of the following is not a unit of energy?
  • a)
    newton meter
  • b)
    electron volt
  • c)
    joule/meter
  • d)
    kilowatt hour
Correct answer is option 'C'. Can you explain this answer?

Gargey Dudhe answered
C is correct option because energy The joule ( symbol: J) is a derived unit of energy in the International System of Units. It is equal to the energy transferred to (or work done on) an object when a force of one newton acts on that object in the direction of its motion through a distance of one metre (1 newton metreor N⋅m). pls upvote and follow me.

When does the potential energy of a spring increase?
  • a)
    only when spring is stretched
  • b)
    only when spring is compressed
  • c)
    when spring is neither stretched nor compressed
  • d)
    when spring is compressed or stretched
Correct answer is option 'D'. Can you explain this answer?

Gaurav Kumar answered
Potential energy of a spring is proportional to the square of the difference of the springs length and its original length, hence whether it is compressed or stretched the potential the potential energy will eventually increase only.

The potential energy of a body at height h is mgh. Then its kinetic energy just before hitting the ground is
  • a)
    mgh
  • b)
  • c)
    mv2
  • d)
Correct answer is option 'A'. Can you explain this answer?

Om Desai answered
From the law of conservation of mechanical energy, the potential energy of a body at height h is converted into kinetic energy when it falls down. So, the magnitude of kinetic energy just before hitting the ground is equal to the potential energy at height h which is mgh.

 Frictional force is an example of
  • a)
    ectrostatic force
  • b)
    Non conservative force
  • c)
    conservative force
  • d)
    nuclear force
Correct answer is option 'B'. Can you explain this answer?

Om Desai answered
The friction is the phenomena that defines that there is a resistance which is present there between the two surfaces. This friction is applied tangentially to the surfaces in contact. Thus the main thing is that the forces on both of the surfaces act tangential to each other.

Select the odd one out
  • a)
    Viscous force
  • b)
    Frictional force
  • c)
    Electrostatic force
  • d)
    Air-resistance
Correct answer is option 'C'. Can you explain this answer?

Anjali Iyer answered
The correct answer is muscular force because all these forces are non-contact forces and muscular force is a contact force. 

Which of the following force is non-conservative
  • a)
    Restoring force of spring
  • b)
    Force between two stationary masses
  • c)
    Force between two stationary charges
  • d)
    Human push or pull
Correct answer is option 'D'. Can you explain this answer?

Anjali Iyer answered
You mean all force that humans apply, or any push/pull force one person does. A conservative force is the property that the work done in moving a particle between two points is independent of the taken path. A conservative force is dependent only on the position of the object. Eg gravity.

For a conservative force, F is equal to
  • a)
  • b)
  • c)
  • d)
Correct answer is option 'C'. Can you explain this answer?

Pooja Shah answered
Potential energy at a point is defined in terms the amount of work done, which is defined in terms of force and thus we get potential as an integral of force applied over some position x. Hence F(x) = -dU(x) / dx which is the differentiation of potential energy wrt position.

 If a force acts perpendicular to the direction of motion of a body, what is the amount of work done?
  • a)
    Infinity
  • b)
    Constant
  • c)
    Zero
  • d)
    sinθ
Correct answer is option 'C'. Can you explain this answer?

Anjali Sharma answered
If a force acts perpendicular to the direction of a body, the amount of work done is zero because there is no displacement in the direction of a force.

For a varying force work done can be expressed as a
  • a)
    product of force and displacement
  • b)
    force divided by the displacement
  • c)
    definite integral of force over displacement
  • d)
    differentiation of force with displacement
Correct answer is option 'C'. Can you explain this answer?

Krishna Iyer answered
For a variable force, the work done can be expressed as a definite integral of force over displacement for any system.In case of a variable force, the is calculated with the help of integration. For example, in the case of a spring, the force acting upon any object attached to a horizontal spring can be given as Fs = -kx, where k is the spring constant and x is the displacement of the object attached. We can see that this force is proportional to the displacement of the object from the equilibrium position, hence the force acting at each instant during the compression and extension of the spring will be different. Thus, the infinitesimally small contributions of work done during each instant are to be counted in order to calculate the total work done.

 If momentum of an object is doubled, how does its kinetic energy change?
  • a)
    increases 4 times
  • b)
    increases 2 times
  • c)
    decreases 4 times
  • d)
    decreases 2 times
Correct answer is option 'A'. Can you explain this answer?

Naina Bansal answered
kinetic energy of object = 1/2 mv2
 
when the momentum of object is doubled,
then, kinetic energy of object = 1/2 m(2v)2
                                           = 1/52 4mv2
                                           = 4[1/2mv2]
so the momentum of an object after doubled is 4 times graeter.

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