Q 11-06-166JEE MainJEE Main 2021 (26 Aug, Shift 2)Medium
The solid cylinder of length $80$ cm and mass $M$ has a radius of $20$ cm. Calculate the density of the material used if the moment of inertia of the cylinder about an axis $CD$ parallel to $AB$ as shown in figure is $2.7$ kg m$^2$.
Answer: (A) $1.49\times10^2$ kg m$^{-3}$
$AB$ is the cylinder's own axis, and $CD$ is parallel to it at distance $\frac{L}{2} = 0.4$ m.
$$I = \frac{1}{2}MR^2 + M(0.4)^2 = M(0.02 + 0.16) = 0.18M = 2.7 \Rightarrow M = 15\ \text{kg}$$
Volume $= \pi R^2L = \pi(0.2)^2(0.8) = 0.1005$ m$^3$.
$$\rho = \frac{15}{0.1005} \approx 1.49\times10^2\ \text{kg m}^{-3}$$
Solution by Sreeraj P, M.Sc Physics