Question

Two wheels are connected by a belt. The radius of the larger wheel is three times that of the smaller one. What is the ratio of the rotational inertia of larger wheel to the smaller wheel, when both wheels have same angular momentum?

• A. $3$
• B. $6$
• C. $9$
• D. $12$

Answer 1

Answer: (A)

As the belt does not slip,

$v_{A}=v_{C}$
i.e., $r_{A}\left(\omega \right)_{A}=r_{C}\left(\omega \right)_{C}\left(\right.\text{ arv }=r\omega \left.\right)\ldots .\left(\right.i\left.\right)$
According to problem, $r_{A}=r$ and $r_{C}=3r$ So, eqn. (i) becomes,
$\omega _{A}=3\omega _{C}$
If both the wheels have same angular momentum
$I_{A}\omega _{A}=I_{C}\omega _{C}$
$\frac{I_{C}}{I_{A}}=\frac{\omega _{A}}{\omega _{C}}=3$