The angular momentum of body remains conserve if :

Options

A. applied force on body is zero.
B. applied torque on body is zero.
C. applied force on body is constant.
D. applied torque on body is constant.

Answer

To determine the conditions under which the angular momentum of a body remains conserved, we need to analyze the relationship between angular momentum and torque.

### Step-by-Step Solution:

1. **Understanding Angular Momentum**:
- Angular momentum (L) of a body is defined as the product of its moment of inertia (I) and its angular velocity (ω). Mathematically, \( L = I \cdot \omega \).

2. **Conservation of Angular Momentum**:
- Angular momentum is said to be conserved when the initial angular momentum (L_i) and the final angular momentum (L_f) are equal, i.e., \( L_i = L_f \).

3. **Relation Between Torque and Angular Momentum**:
- The torque (τ) acting on a body is defined as the rate of change of angular momentum. This can be expressed mathematically as:
\[ \tau = \frac{dL}{dt} \]
- This means that if there is a net torque acting on the body, it will cause a change in angular momentum.

4. **Condition for Conservation**:
- For angular momentum to remain constant (conserved), the change in angular momentum must be zero:
\[ \Delta L = L_f - L_i = 0 \]
- From the torque equation, if \( \Delta L = 0 \), then:
\[ \tau = 0 \]
- This indicates that for angular momentum to be conserved, the net torque acting on the body must be zero.

5. **Evaluating the Options**:
- Given the options:
- (A) Applied torque force is 0
- (B) Applied torque on the body is 0
- (C) Applied force is constant
- (D) Applied torque is constant
- The correct option is (B) "Applied torque on the body is 0" since this directly relates to the condition for conservation of angular momentum.

### Conclusion:
The angular momentum of a body remains conserved if the applied torque on the body is zero.

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