Question

A brass disc is rotating about its axis. If temperature of the disc is increased then its:

• A. radius of gyration increases, but moment of inertia remains the same
• B. moment of inertia increases but radius of gyration 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

Answer 1

The correct option is D radius of gyration and moment of inertia both increases

Radius of gyration and
moment of inertia will increase.
$\because I=m{k}^2$
$k=\sqrt{\frac{I}{m}}$
$I=\frac{m{R}^2}{2}$
$k=\frac{R}{\sqrt{2}}$
$A=A_0(1+2\alpha \Delta T)(e{q}^n$ of thermal expansion)
$\pi r^2=\pi R_0^2(1+2\alpha \Delta T)$
$r^2=R_0^2(1+2\alpha \Delta T)$
$\therefore$ r will increase on increasing the temperature
$\therefore Iandk$ will increase on increasing the $temperature$