NEET System of Particles and Rotational Motion — Set 16

Question 1

Which statement is true about the axis of rotation in pure rotational motion?

Accepted Answer

In pure rotational motion, the axis of rotation is fixed, meaning it does not move or change direction, constraining the body to rotate about it.

Question 2

A wheel with moment of inertia $ 2.5 \, \text{kg m}^2 $ rotates at $ 6 \, \text{rad/s} $. A torque of $ 10 \, \text{Nm} $ acts for $ 2 \, \text{s} $. What is its final angular velocity?

Accepted Answer

$ \alpha = \frac{\tau}{I} = \frac{10}{2.5} = 4 \, \text{rad/s}^2 $. $ \Delta \omega = \alpha t = 4 \times 2 = 8 \, \text{rad/s} $. $ \omega = \omega_0 + \Delta \omega = 6 + 8 = 14 \, \text{rad/s} $.

Question 3

A $ 6 \, \text{kg} $ object moves with a velocity of $ 3 \, \hat{\mathbf{i}} - 2 \, \hat{\mathbf{j}} \, \text{m/s} $. What is the magnitude of the velocity of its center of mass?

Accepted Answer

For a single object, the center of mass velocity equals the object’s velocity. Magnitude = $ \sqrt{(3)^2 + (-2)^2} = \sqrt{9 + 4} = \sqrt{13} \approx 3.6 \, \text{m/s} $.

NEET Physics: System of Particles and Rotational Motion — Practice Set 16

Q1. Which statement is true about the axis of rotation in pure rotational motion?

Q2. A wheel with moment of inertia \( 2.5 \, \text{kg m}^2 \) rotates at \( 6 \, \text{rad/s} \). A torque of \( 10 \, \text{Nm} \) acts for \( 2 \, \text{s} \). What is its final angular velocity?

Q3. A \( 6 \, \text{kg} \) object moves with a velocity of \( 3 \, \hat{\mathbf{i}} - 2 \, \hat{\mathbf{j}} \, \text{m/s} \). What is the magnitude of the velocity of its center of mass?

Q4. A wheel of radius \( 0.4 \, \text{m} \) and moment of inertia \( 1.6 \, \text{kg m}^2 \) is accelerated by a torque of \( 8 \, \text{Nm} \). What is its angular acceleration?

Q5. What is the SI unit of moment of inertia?

Q6. A force \( \mathbf{F} = -3 \, \hat{\mathbf{i}} - 4 \, \hat{\mathbf{j}} \, \text{N} \) acts at \( \mathbf{r} = 2 \, \hat{\mathbf{i}} + 5 \, \hat{\mathbf{j}} \, \text{m} \). What is the magnitude of the torque about the origin?

Q7. Two particles of masses \( 2 \, \text{kg} \) and \( 8 \, \text{kg} \) are at \( (1, 5) \) and \( (4, 1) \) respectively. What is the distance of their center of mass from the origin?

Q8. A disk with moment of inertia \( 1.5 \, \text{kg m}^2 \) rotates at \( 4 \, \text{rad/s} \). A torque of \( 6 \, \text{Nm} \) acts for \( 3 \, \text{s} \). What is its final angular velocity?

Q9. Two particles of masses \( 4 \, \text{kg} \) and \( 6 \, \text{kg} \) are at \( (2, 0) \) and \( (0, 3) \) respectively. What is the distance of their center of mass from \( (0, 0) \)?

Q10. A torque of \( 21 \, \text{Nm} \) acts on a wheel with moment of inertia \( 7 \, \text{kg m}^2 \) starting from rest. What is its angular speed after \( 4 \, \text{s} \)?