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Question

A brass disc is rotating about its axis. If temperature of the disc is increased then its:
  1. radius of gyration increases, but moment of inertia remains the same
  2. moment of inertia increases but radius of gyration remains the same
  3. radius of gyration and moment of inertia both remain the same
  4. radius of gyration and moment of inertia both increases

A
moment of inertia increases but radius of gyration remains the same
B
radius of gyration increases, but moment of inertia remains the same
C
radius of gyration and moment of inertia both remain the same
D
radius of gyration and moment of inertia both increases
Solution
Verified by Toppr

Radius of gyration and
moment of inertia will increase.
I=mk2
k=Im
I=mR22
k=R2
A=A0(1+2αΔT)(eqn of thermal expansion)
πr2=πR20(1+2αΔT)
r2=R20(1+2αΔT)
r will increase on increasing the temperature
I and k will increase on increasing the temperature

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