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A torque of 2 newton-m produces an angular acceleration of 2 rad/sec2 a body. If its radius of gyration is 2m, its mass will be:
  • a)
    2 kg
  • b)
    4 kg
  • c)
    1/2 kg
  • d)
    1/4 kg
Correct answer is option 'B'. Can you explain this answer?
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A torque of 2 newton-m produces an angular acceleration of 2 rad/sec2a...
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A torque of 2 newton-m produces an angular acceleration of 2 rad/sec2a...
Given: Torque (τ) = 2 N-m, angular acceleration (α) = 2 rad/sec2, radius of gyration (k) = 2 m

To find: Mass (m)

Formula used: τ = Iα, where I = mk2 (moment of inertia)

Calculation:

- Moment of inertia (I) = mk2 = τ/α * k2
- Substituting the given values, we get:
I = 2/2 * 22 = 8 kg-m2
- Mass (m) = I/k2 = 8/22 = 4 kg

Therefore, the mass of the body is 4 kg.
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