System of Particles & Rotational Motion Test

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System of Particles & Rotational Motion Test - 12

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Question 1
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Kinetic energy of a rolling object is the

A
work done on moving the object from infinity to that point

B
translational kinetic energy

C
rotational kinetic energy

D
sum of translational kinetic energy and rotational kinetic energy

Solution

If an object is rolling without slipping, then its kinetic energy can be expressed as the sum of the translational kinetic energy of its center of mass plus the rotational kinetic energy about the center of mass.
Question 2
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A rotating machine is maintained at a uniform angular speed of 150 rad s^-1, with a torque of 100 Nm. The power is

A
15 kW

B
1.5 kW

C
1500 kW

D
0.15 kW

Solution

Power = torque × angular velocity
P = 100 × 150
P = 15000 W
P = 15KW
Question 3
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If we apply Newton’s First Law to torque then the statement will be

A
If the net torque acting on a rigid object is zero, it will rotate with a non-uniform angular velocity

B
If the net torque acting on a rigid object is non zero, it will rotate with a constant angular velocity

C
If the net torque acting on a rigid object is zero, it will rotate with a constant angular velocity

D
If the net torque acting on a rigid object is non zero, it will rotate with a non-uniform angular velocity

Solution

Newton's First Law for Rotation: an object at rest tends to remain at rest, and an object that is spinning tends to spin with a constant angular velocity, unless it is acted on by a nonzero net torque or there is a change in the way the object's mass is distributed.
Question 4
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A torque of 20 Nm is applied to a flywheel of mass 10 kg and radius of gyration 50 cm. The resulting angular acceleration is:

A
4 rads^-2

B
10 rads^-2

C
6 rads^-2

D
8 rads^-2
Question 5
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In case of couples, which statement is not true?

A
Couple can be balanced by a single force.

B
The sum of moment of all forces about any point is same.

C
Couple is always balanced by a couple.

D
Couple cannot be balanced by a single force.

Solution

When two forces of equal magnitude opposite in direction and acting along parallel straight lines, then they are said to form a couple. The perpendicular distance between the two force forming a couple is called the arm of the couple.
‘Couple’ are the types of forces acting clockwise or anti-clockwise. We can only balance them by two forces minimum.
Question 6
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A rigid body is rotating about an axis. Different particles are at different distances from the axis. Which of the following is true?

A
Different particles possess the same angular acceleration

B
Different particles possess the same angular velocity

C
Different particles possess the same linear acceleration

D
Different particles possess the same linear velocity.

Solution

In the fixed axis rotation we see that every point on the body has two components of velocity, one in the radial direction and one in the tangential direction. The resultant of these velocities is not the same for any two points lying in the plane of the body.
Any two points on the radial line have the radial acceleration directed towards the center of equal magnitude and the tangential acceleration of equal magnitude as well. Thus option B is correct.
All the particles lying on the curved surface of a cylinder whose axis coincides with the axis of rotation have the same speed but different velocities.
Question 7
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To maximize torque on a lever, which of the following will not help?

A
Apply the force in a direction perpendicular to the lever

B
Increasing the magnitude of the force, F that we apply

C
Increasing the distance, r, from the axis of rotation of the point to which you apply the force

D
Increasing the density of material.
Question 8
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Kinetic Energy of a rotating body i.e. Rotational Kinetic Energy can be converted to various forms of energy they are

A
Heat, Potential Energy

B
Linear Kinetic Energy, Potential Energy

C
Heat, Linear Kinetic Energy, Potential Energy

D
Heat, Linear Kinetic Energy

Solution

Take an example where the system is attached with spring and the spring is attached to a wall, if you rotate the system that system has KE and spring will also rotate with that system and thus spring will start to compress which will create PE in it and heat will obviously be generated.
Question 9
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A 2 m rod of mass 1 kg rotates at an angular speed of 15 rad/s about its ends. Then K.E. is

A
150 J

B
1500 J

C
100 J

D
1.5 J

Solution

Given,
l=2m
m=1kg
ω=15rd//s
K.E.=1/2I ω
=1/2x(ml²/3) ω²
=1/2x(1x4/3)(15)²
=150J
Question 10
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An object is in combined rotational and translational motion. Its K.E. is

A

B

C

D

Solution

Total kinetic energy =