Question

(A): A solid sphere $(\alpha =20\times {10}^{-4}{/}^{\circ }C)$ of radius $r$ is spinning about its diameter as axis with an angular speed $w$. If the temperature of sphere increases by 100C, the ratio of new angular speed to original angular speed is 25:26
(B): Moment of inertia $I\propto \omega$

• A. A and B are correct and B is correct explanation for A
• B. A and B are correct and B is not correct explanation for A
• C. A is true and B is false
• D. A is wrong and B is true.

Answer 1

The correct option is C A is true and B is false

Reason is clearly false because moment of inertia does not depend on angular velocity.
Now for assertion, increase in radius will be
$\Delta R=R\alpha \Delta \theta$
$\Delta R=R\times 20\times {10}^{-4}\times 100$
$\Delta R=0.02R$
$R^{\prime }=R+\Delta R$
$R^{\prime }=1.02R$
Initial MI be $I$ then new MI will be $(1.02{)}^{2}I$
New $MI=1.0404I$
Since angular momentum is conserved
$I_1{\omega }_1=I_2{\omega }_2$
${\omega }_1/{\omega }_2=I_2/I_1$
${\omega }_1/{\omega }_2=1.0404=26/25$
Therefore, ${\omega }_2/{\omega }_1=25/26$
Assertion is true