If the unit of mass , length and the time are doubled then unit of angular momentum will be

Options

A. Doubled
B. Tripled
C. Quadrupled
D. Eight times

Answer

To solve the problem, we need to analyze how the units of angular momentum change when the units of mass, length, and time are doubled.

### Step 1: Understand the formula for angular momentum
The angular momentum \( L \) is given by the formula:
\[ L = M \cdot V \cdot R \]
where:
- \( M \) is mass,
- \( V \) is linear velocity,
- \( R \) is the radius (or distance from the axis of rotation).

### Step 2: Identify how the units change
If the units of mass, length, and time are doubled:
- New mass unit \( M' = 2M \)
- New length unit \( R' = 2R \)
- New time unit \( T' = 2T \)

### Step 3: Determine how velocity changes
Velocity \( V \) is defined as:
\[ V = \frac{R}{T} \]
When the units of length (R) are doubled and the units of time (T) are also doubled, the new velocity \( V' \) can be calculated as follows:
\[ V' = \frac{R'}{T'} = \frac{2R}{2T} = \frac{R}{T} = V \]
This means that the velocity remains unchanged.

### Step 4: Substitute the new values into the angular momentum formula
Now we substitute the new values into the angular momentum formula:
\[ L' = M' \cdot V' \cdot R' = (2M) \cdot V \cdot (2R) \]
This simplifies to:
\[ L' = 2M \cdot V \cdot 2R = 4 \cdot (M \cdot V \cdot R) = 4L \]

### Step 5: Conclusion
Thus, the new unit of angular momentum \( L' \) is four times the original unit of angular momentum \( L \):
\[ L' = 4L \]

### Final Answer
The unit of angular momentum will be quadrupled, or 4 times the original unit.

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