Question

If the temperature of a uniform rod is slightly increased by ∆t, its moment of inertia I about a line parallel to itself will increase by
(a) zero
(b) αI∆t
(c) 2αI∆t
(d) 3αI∆t.

Answer 1

If the temperature of a uniform rod is slightly increased by ∆t, its moment of inertia I about a line parallel to itself will increase by 2αI∆t

Option: (c)

Explanation:

• With the change in temperature, the change in the moment of inertia of a solid body of any shape is as follows,
• I’=I1+2αΔt
• Where,  
• Initial moment of inertia = I  
• New moment of inertia due to change in temperature = I’  
• Coefficient of expansion = α  
• When the temperature is increased by ∆t, where Δt is the change in temperature
• So, I’-I=2αIΔt
• Hence, 2αIΔt is the correct answer.