Two loops ' $A$ ' and ' $B$ ' of radii ' $R_1$ ' and ' $R_2$ ' are made from uniform wire. If moment of inertia of ' A ' is ' $\mathrm{I}_{\mathrm{A}}$ ' and that ' B ' is ' $\mathrm{I}_{\mathrm{B}}$ ', then $\mathrm{R}_2 / \mathrm{R}_1$ is $\left[\frac{\mathrm{I}_{\mathrm{A}}}{\mathrm{I}_{\mathrm{B}}}=27\right]$
In case of rotational dynamics, which one of the following statements is correct?
[$\vec{\omega}=$ angular velocity, $\overrightarrow{\mathrm{v}}=$ linear velocity
$\overrightarrow{\mathbf{r}}=$ radius vector, $\vec{\alpha}=$ angular acceleration
$\overrightarrow{\mathrm{a}}=$ linear acceleration, $\overrightarrow{\mathrm{L}}=$ angular momentum
$\overrightarrow{\mathrm{p}}=$ linear momentum, $\bar{\tau}=$ torque,
$\overrightarrow{\mathrm{f}}=$ centripetal force]
Ratio of radius of gyration of a circular disc to that of circular ring each of same mass and radius around their respective axes is
Two circular loops P and Q of radii ' r ' and ' nr ' are made respectively from a uniform wire. Moment of inertia of loop Q about its axis is four times that of loop P about its axis. The value of ' $n$ ' is