Question

If the temperature of a uniform rod is slightly increased by ∆t, its moment of inertia I about a perpendicular bisector increases by
(a) zero
(b) αI∆t
(c) 2αI∆t
(d) 3αI∆t.

Answer 1

(c) 2αI∆t

• Explanation:
• With the change in temperature, the change in the moment of inertia of a uniform rod is as follows,
• I’=I(1+2αΔt)
• Where,  
• Initial moment of inertia = I  
• New moment of inertia due to the change in temperature = I’  
• Coefficient of expansion = α
• When the temperature is increased by ∆t, then the increase in length is,
• Where, change in temperature = ∆t  
• Therefore, I’-I=2αIΔt
• Hence, 2αIΔt is the correct answer.