A body is acted upon by a constant torque . In 4 seconds its angular momentum changes from L to 4L . The magnitude of the torque is

Options

A. `(L)/(4)`
B. `(3L)/(4)`
C. 3L
D. 12L

Explanation

To find the magnitude of the torque acting on the body, we can use the relationship between torque and angular momentum. The torque (τ) is defined as the rate of change of angular momentum (L) with respect to time (t).

### Step-by-Step Solution:

1. **Understand the Change in Angular Momentum**:
- The initial angular momentum (L1) is L.
- The final angular momentum (L2) is 4L.
- The change in angular momentum (ΔL) can be calculated as:
\[ \Delta L = L2 - L1 = 4L - L = 3L \]

2. **Determine the Time Interval**:
- The time interval (Δt) over which this change occurs is given as 4 seconds.

3. **Use the Torque Formula**:
- The torque (τ) is given by the formula:
\[ \tau = \frac{\Delta L}{\Delta t} \]
- Substituting the values we calculated:
\[ \tau = \frac{3L}{4 \text{ seconds}} \]

4. **Calculate the Magnitude of the Torque**:
- Therefore, the magnitude of the torque is:
\[ \tau = \frac{3L}{4} \]

5. **Final Answer**:
- The magnitude of the torque is \(\frac{3L}{4}\).