The moment of inertia of a disc of radius 0.5m about its geometric axis is 2kg-`m^(2)` . If a string is tied to its circumference and a force of 10 Newton is applied, the value of torque with respect to this axis will be:

Options

A. 2.5 N-m
B. 5 N-m
C. 10 N-m
D. 20 N-m

Answer

To solve the problem, we need to calculate the torque exerted on the disc when a force is applied. The torque (τ) can be calculated using the formula:

\[ \tau = r \times F \]

where:
- \( r \) is the radius of the disc,
- \( F \) is the force applied.

### Step 1: Identify the given values
- Radius of the disc, \( r = 0.5 \, m \)
- Force applied, \( F = 10 \, N \)

### Step 2: Substitute the values into the torque formula
Using the formula for torque:

\[ \tau = r \times F \]

Substituting the known values:

\[ \tau = 0.5 \, m \times 10 \, N \]

### Step 3: Calculate the torque
Now, perform the multiplication:

\[ \tau = 5 \, N \cdot m \]

### Conclusion
The value of torque with respect to the geometric axis of the disc is:

\[ \boxed{5 \, N \cdot m} \]

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