Question 453: Centre of Mass and Rotational Motion

Question

In the given figure, two wheels P and Q are connected by a belt B. The radius of P is three times as that of Q. In case of same rotational kinetic energy, the ratio of rotational inertias $$\left( {{{{I_1}} \over {{I_2}}}} \right)$$ will be x : 1. The value of x will be _____________.

Accepted Answer

$${1 \over 2}{I_1}{({\omega _1})^2} = {1 \over 2}{I_2}{({\omega _2})^2}$$
$${I_1}{\left( {{v \over {3R}}} \right)^2} = {I_2}{\left( {{v \over R}} \right)^2}$$
$${{{I_1}} \over {{I_2}}} = {9 \over 1}$$

Centre of Mass and Rotational Motion

In the given figure, two wheels P and Q are connected by a belt B. The radius of P is three times as that of Q. In case of same rotational kinetic energy, the ratio of rotational inertias $\left( {{{{I_1}} \over {{I_2}}}} \right)$ will be x : 1. The value of x will be _____________.

Integer / Numeric Answer Type