System of Particles and Rotational Motion Chapter-Wise Test 10

Correct answer Carries: 4.

Wrong Answer Carries: -1.

Which factor does not affect the moment of inertia of a rigid body?

Moment of inertia (\( I = \sum m_i r_i^2 \)) depends on mass and its distribution about the axis, not on angular velocity, which affects motion but not \( I \).

Mass of the body
Distribution of mass
Angular velocity
Axis of rotation
3

A solid sphere of mass \( 1 \, \text{kg} \) and radius \( 0.5 \, \text{m} \) has a kinetic energy of \( 5 \, \text{J} \). What is its angular speed?

\( I = \frac{2}{5} M R^2 = \frac{2}{5} \times 1 \times (0.5)^2 = 0.1 \, \text{kg m}^2 \).

\( K = \frac{1}{2} I \omega^2 \Rightarrow 5 = \frac{1}{2} \times 0.1 \times \omega^2 \Rightarrow 10 = 0.1 \omega^2 \Rightarrow \omega^2 = 100 \Rightarrow \omega = 10 \, \text{rad/s} \).

8 rad/s
10 rad/s
12 rad/s
14 rad/s
2

A solid cylinder with moment of inertia \( 2 \, \text{kg m}^2 \) is acted upon by a torque of \( 10 \, \text{Nm} \). What is its angular acceleration?

\( \tau = I \alpha \).

\( \tau = 10 \, \text{Nm} \), \( I = 2 \, \text{kg m}^2 \).

\( \alpha = \frac{\tau}{I} = \frac{10}{2} = 5 \, \text{rad/s}^2 \).

4 rad/s²
5 rad/s²
6 rad/s²
7 rad/s²
2

A hollow cylinder of mass \( 2 \, \text{kg} \) and radius \( 0.8 \, \text{m} \) has an angular momentum of \( 16 \, \text{kg m}^2/\text{s} \). What is its angular velocity?

\( I = M R^2 = 2 \times (0.8)^2 = 1.28 \, \text{kg m}^2 \).

\( \omega = \frac{L}{I} = \frac{16}{1.28} = 12.5 \, \text{rad/s} \).

11 rad/s
12 rad/s
12.5 rad/s
13 rad/s
3

A \( 1 \, \text{kg} \) mass rotates in a circle of radius \( 0.9 \, \text{m} \) with a speed of \( 6 \, \text{m/s} \). What is its angular momentum about the center?

\( L = m v r \).

\( m = 1 \, \text{kg} \), \( v = 6 \, \text{m/s} \), \( r = 0.9 \, \text{m} \).

\( L = 1 \times 6 \times 0.9 = 5.4 \, \text{kg m}^2/\text{s} \).

5.0 kg m²/s
5.4 kg m²/s
5.8 kg m²/s
6.0 kg m²/s
2

What is the rotational analogue of mass in Newton’s second law?

In Newton’s second law for rotation (\( \mathbf{\tau} = I \mathbf{\alpha} \)), moment of inertia \( I \) is the rotational analogue of mass, representing resistance to angular acceleration.

Torque
Angular velocity
Moment of inertia
Angular momentum
3

Which property of a rigid body remains constant during rotation about a fixed axis?

For a rigid body rotating about a fixed axis, all particles have the same angular velocity, which is a property of the body’s rotation and remains constant across all points.

Linear velocity
Angular velocity
Linear acceleration
Mass distribution
2

A thin ring of mass \( 5 \, \text{kg} \) and radius \( 0.2 \, \text{m} \) rotates at \( 10 \, \text{rad/s} \). What is its angular momentum?

\( I = M R^2 = 5 \times (0.2)^2 = 0.2 \, \text{kg m}^2 \).

\( L = I \omega = 0.2 \times 10 = 2 \, \text{kg m}^2/\text{s} \).

1.5 kg m²/s
2 kg m²/s
2.5 kg m²/s
3 kg m²/s
2

A torque of \( 15 \, \text{Nm} \) acts on a wheel with moment of inertia \( 5 \, \text{kg m}^2 \) starting from rest. What is its angular speed after \( 3 \, \text{s} \)?

\( \alpha = \frac{\tau}{I} = \frac{15}{5} = 3 \, \text{rad/s}^2 \).

\( \omega = \omega_0 + \alpha t = 0 + 3 \times 3 = 9 \, \text{rad/s} \).

7 rad/s
9 rad/s
11 rad/s
13 rad/s
2

A hollow cylinder of mass \( 2 \, \text{kg} \) and radius \( 0.5 \, \text{m} \) has an angular momentum of \( 10 \, \text{kg m}^2/\text{s} \). What is its angular velocity?

\( I = M R^2 = 2 \times (0.5)^2 = 0.5 \, \text{kg m}^2 \).

\( \omega = \frac{L}{I} = \frac{10}{0.5} = 20 \, \text{rad/s} \).

15 rad/s
18 rad/s
20 rad/s
25 rad/s
3

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