Q 11-06-112JEE MainJEE Main 2023 (25 Jan, Shift 2)Medium
If a solid sphere of mass $5\ \text{kg}$ and a disc of mass $4\ \text{kg}$ have the same radius, then the ratio of moment of inertia of the disc about a tangent in its plane to the moment of inertia of the sphere about its tangent will be $\dfrac x7$. The value of $x$ is ______.
Numerical value type. Enter your answer.
Answer: 5
Disc, tangent in its plane: $\dfrac14MR^2+MR^2=\dfrac54MR^2=\dfrac54(4)R^2=5R^2$.
Sphere, tangent: $\dfrac25MR^2+MR^2=\dfrac75(5)R^2=7R^2$.
Ratio $=\dfrac57$, so $x=5$.
Solution by Sreeraj P, M.Sc Physics