Question

By keeping moment of inertia of a body constant, if we double the time period, then angular momentum of body

• A. remains constant
• B. becomes half
• C. doubles
• D. quadruples

Answer 1

Answer: (B)

becomes half

Answer 2

We know that angular momentum of the body is given by
$L=I \omega$
or $L=I\times \frac{2 \pi}{\tau}$
or $L \propto \frac{1}{T}$
$\Rightarrow \frac{L_1}{L_2}=\frac{T_2}{T_1}$
$\frac{L}{L_2}=\frac{2T}{T} (As ,T_2=2T)$
so,$L_2=\frac{L}{2}$ Thus, on doubling the time period, angular momentum of body becomes half.