These MCQs provide a comprehensive overview of the core concepts associated with the system of particles and rotational motion. Understanding these principles and their applications forms the bedrock for advanced studies in physics. Each question is complemented by the correct answer and a concise explanation.

## 1. The moment of inertia of a point mass about an axis of rotation is proportional to:

### Answer:

### Explanation:

The moment of inertia (I) of a point mass (m) about an axis of rotation is given by I = m * r^2, where r is the distance from the axis.

## 2. If no external torque acts on a closed system, which of the following remains constant?

### Answer:

### Explanation:

According to the law of conservation of angular momentum, if no external torque acts on a closed system, its angular momentum remains constant.

## 3. The motion of a wheel rolling without slipping is an example of:

### Answer:

### Explanation:

When a wheel rolls without slipping, it moves forward (translation) and simultaneously rotates about its axis.

## 4. For a fixed applied force, which shape will have the least angular acceleration?

### Answer:

### Explanation:

For a given torque, angular acceleration is inversely proportional to the moment of inertia. A thin ring has the highest moment of inertia among the listed shapes for a fixed mass and radius.

## 5. Which statement is false about the center of mass?

### Answer:

### Explanation:

The motion of the center of mass of a system is unaffected by the internal forces acting within the system.

## 6. A rigid body rotates about a fixed axis. Which quantity will always remain constant?

### Answer:

### Explanation:

If no external torque acts on the rigid body, its angular momentum remains conserved.

## 7. The rotational analogue of mass is:

### Answer:

### Explanation:

Just as mass is a measure of resistance to linear acceleration, the moment of inertia is a measure of resistance to angular acceleration.

## 8. The radius of gyration of a body about an axis is:

### Answer:

### Explanation:

Radius of gyration gives a measure of distribution of the mass of the body about the axis of rotation.

## 9. In a merry-go-round motion, a person standing at the center has:

### Answer:

### Explanation:

The linear velocity is zero at the center but the angular velocity is the same everywhere on a rotating platform.

## 10. A fan blade, initially at rest, reaches an angular speed ω in time t. If the net external torque is constant, the angular acceleration is:

### Answer:

### Explanation:

Angular acceleration, α = change in angular velocity / time taken = ω/t.

## 11. The quantity which remains unchanged during pure rotational motion is:

### Answer:

### Explanation:

In pure rotational motion, all particles of the body move in circles with the same angular speed.

## 12. For a given torque on a system, if the moment of inertia is doubled, the angular acceleration:

### Answer:

### Explanation:

Angular acceleration (α) is inversely proportional to the moment of inertia (I). If I doubles, α becomes half.

## 13. If the net external torque applied on a system is zero, which of the following is conserved?

### Answer:

### Explanation:

According to the conservation principle, when no external torque acts on a system, its angular momentum remains conserved.

## 14. A solid sphere and a hollow sphere have the same mass and radius. Which one has a greater moment of inertia about an axis passing through its center and perpendicular to its plane?

### Answer:

### Explanation:

The moment of inertia for a solid sphere (I = 2/5 m*r^2) is less than that of a hollow sphere (I = 2/3 m*r^2) when both have the same mass and radius.

## 15. The torque τ acting on a body is related to the moment of inertia I and angular acceleration α by:

### Answer:

### Explanation:

Torque is the rotational analogue of force. The relation τ = Iα is analogous to F = ma in linear motion.