Question

A raw egg and hard boiled egg are made to spin on a table with the same angular momentum about the same axis. The ratio of the time taken by the two to stop is

• A. $=1$
• B. $<1$
• C. $>1$
• D. None of these

Answer 1

The correct option is B $<1$

So raw egg is like a spherical shell & hard boiled egg is like solid sphere. Let $I_1,I_2$ be Moment of Inertia of raw egg and boiled egg respectively.
Given that angular momentum $L$, is same
$\therefore I_1{\omega }_1=I_2{\omega }_2\Rightarrow {\omega }_2>{\omega }_1\because I_1>I_2$
From the first equation of angular motion $({\omega }_t={\omega }_1+\alpha t)$ where $\alpha$ is deceleration for both cases
& ${\omega }_f=0$ for both cases.
Hence, $\frac{t_1\text{(raw egg)}}{t_2\text{(hard egg)}}=\frac{{\omega }_1/\alpha }{{\omega }_2/\alpha }\Rightarrow \frac{t_1}{t_2}<1$