A torque of 2 newton-m produces an angular acceleration of `2 rad//sec^(2)` a body. If its radius of gyration is 2m, its mass will be:

Options

A. (a)2kg
B. (b)4kg
C. (c)1/2kg
D. (d)1/4kg

Answer

To find the mass of the body given the torque, angular acceleration, and radius of gyration, we can follow these steps:

### Step 1: Understand the relationship between torque, moment of inertia, and angular acceleration.
The torque (\( \tau \)) is related to the moment of inertia (\( I \)) and angular acceleration (\( \alpha \)) by the formula:
\[ \tau = I \cdot \alpha \]

### Step 2: Express moment of inertia in terms of mass and radius of gyration.
The moment of inertia (\( I \)) can be expressed in terms of mass (\( m \)) and radius of gyration (\( k \)) as:
\[ I = m \cdot k^2 \]

### Step 3: Substitute the expression for moment of inertia into the torque equation.
Substituting \( I \) in the torque equation:
\[ \tau = (m \cdot k^2) \cdot \alpha \]

### Step 4: Rearrange the equation to solve for mass.
Rearranging the equation to solve for mass (\( m \)):
\[ m = \frac{\tau}{k^2 \cdot \alpha} \]

### Step 5: Substitute the given values into the equation.
We have:
- Torque (\( \tau \)) = 2 N·m
- Radius of gyration (\( k \)) = 2 m
- Angular acceleration (\( \alpha \)) = 2 rad/s²

Substituting these values:
\[ m = \frac{2}{(2)^2 \cdot 2} \]

### Step 6: Calculate the mass.
Calculating the denominator:
\[ (2)^2 = 4 \quad \text{and} \quad 4 \cdot 2 = 8 \]
Now substituting back:
\[ m = \frac{2}{8} = \frac{1}{4} \text{ kg} \]

### Conclusion
The mass of the body is \( \frac{1}{4} \) kg.