The torque needed to produce an angular acceleration of 18rad/`"sec"^2` in a body of moment of inertia 2.5kg-`m^2` would be -

Options

A. 4.5 newton-metre
B. 45 newton-metre
C. `4.5 xx 10^2` newton - metre
D. `45 xx10^(-2)` newton - metre

Answer

To find the torque needed to produce an angular acceleration in a body with a given moment of inertia, we can use the following formula:

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Moment of Inertia (I) = 2.5 kg·m²
- Angular Acceleration (α) = 18 rad/s²

2. **Use the Torque Formula**:
The formula for torque (τ) is given by:
\[ \tau = I \cdot \alpha \]
where:
- τ is the torque,
- I is the moment of inertia,
- α is the angular acceleration.

3. **Substitute the Values into the Formula**:
Substitute the known values into the torque formula:
\[ \tau = 2.5 \, \text{kg·m²} \cdot 18 \, \text{rad/s²} \]

4. **Calculate the Torque**:
Perform the multiplication:
\[ \tau = 2.5 \cdot 18 = 45 \, \text{N·m} \]

5. **Conclusion**:
The torque needed to produce an angular acceleration of 18 rad/s² in a body with a moment of inertia of 2.5 kg·m² is:
\[ \tau = 45 \, \text{N·m} \]

### Final Answer:
The torque needed is **45 N·m**.

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