Physics Test 186

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Physics Test 186

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Question 1
4 / -1

A circular disc A of radius r is made from an iron plate of thickness t, and another circular disc B of radius 4r is made from an iron plate of thickness t/4. The relation between the moments of inertia I_A and I_B is

A
I_A > I_B

B
I_A = I_B

C
I_A < I_B

D
depends on the actual values of t and r.

Solution

First of all, we will find the mass of the disc which can be found by the fornula

mass = density * volume

Volume = R² (t = thickness)

density = ρ
Question 2
4 / -1

A solid homogeneous sphere is moving on a rough horizontal surface, partly rolling and partly sliding. During this kind of motion of the sphere

A
total kinetic energy is conserved

B
angular momentum of the sphere about the point of contact with the plane is conserved

C
only the rotational kinetic energy about the centre of mass is conserved

D
angular momentum about centre of mass is conversed

Solution

Angular momentum about point of contact is conserved because torque due to friction about point of contact will be zero.
Question 3
4 / -1

A sphere of mass m and radius r rolls on a horizontal plane without slipping with the speed u. Now, if it rolls up vertically, the maximum height it would attain will be

A

B

C

D

Solution

The rolling sphere has rotational as well as translational kinetic energy.
Question 4
4 / -1

The wheels on the old-time bicycle shown in the diagram have radii of 60.0 cm. and 10.0 cm. If the larger wheel is rotating at 12.0 rad s^-1, what is the angular speed of the smaller wheel?

A
12.0 rad s⁻¹

B
60.0 rad s⁻¹

C
72.0 rad s⁻¹

D
2.0 rad s⁻¹

Solution

The linear velocity of both wheels will be the same

60 × 12 = 10×ω

ω = 72 rad s⁻¹
Question 5
4 / -1

Angular momentum is conserved

A
always

B
never

C
when external force is absent

D
when external torque is absent

Solution

According to the law of conservation of angular momentum, if there is no external torque on the system, then the angular momentum remains constant.
Question 6
4 / -1

If the earth shrinks such that its mass does not change but radius decreases to one-quarter of its original value then one complete day will take

A
96 h

B
48 h

C
6 h

D
1.5 h

Solution
Question 7
4 / -1

A solid sphere rolls down two different inclined planes of same height, but of different inclinations. In both cases,

A
Speed and time of descent will be same

B
Speed will be same, but time of descent will be different

C
Speed will be different, but time of descent will be same

D
Speed and time of descent both are different

Solution

In pure rolling, mechanical energy remains conserved. Therefore, when heights of inclines are equal, speed of sphere will be same in both the cases. But as acceleration down the plane, a ∝ sinθ therefore, acceleration and time of descent will be different
Question 8
4 / -1

The angular speed of rotating rigid body is increased from 4ω to 5ω keeping moment of inertia constant. The percentage increase in its K.E is -

A
20%

B
25%

C
125%

D
56%

Solution
Question 9
4 / -1

The radius of a solid sphere is R and its density D. When it is made to rotate about an axis passing through any diameter of sphere, expression for its moment of inertia is

A

B

C

D

Solution
Question 10
4 / -1

The equation τ = Iα is valid about which of the following?

A
Centre of mass of the body

B
Axis of rotation

C
Both Center of mass and axis of rotation

D
All the points

Solution

The equation τ = Iα is valid about COM or axis of rotation but not about any other point.