Two spheres of equal masses,one of which is a | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Let the radii of the thin spherical shell and the solid sphere be $R_1$ and $R_2$,respectively.The moment of inertia of a thin spherical shell abo

Vedclass · Accepted Answer

$\sqrt{3}: \sqrt{5}$

Vedclass · Answer

(B) Let the radii of the thin spherical shell and the solid sphere be $R_1$ and $R_2$,respectively.The moment of inertia of a thin spherical shell about its diameter is given by:$I_{	ext{shell}} = \frac{2}{3} MR_1^2$ ... $(i)$The moment of inertia of a solid sphere about its diameter is given by:$I_{	ext{sphere}} = \frac{2}{5} MR_2^2$ ... (ii)Given that the masses $(M)$ and the moments of inertia $(I)$ for both bodies are equal,we equate $(i)$ and (ii):$\frac{2}{3} MR_1^2 = \frac{2}{5} MR_2^2$Dividing both sides by $M$ and simplifying:$\frac{R_1^2}{R_2^2} = \frac{3}{5}$Taking the square root on both sides:$\frac{R_1}{R_2} = \frac{\sqrt{3}}{\sqrt{5}}$Thus,the ratio of their radii is $\sqrt{3}: \sqrt{5}$.

Two spheres of equal masses,one of which is a thin spherical shell and the other a solid sphere,have the same moment of inertia about their respective diameters. The ratio of their radii is

Similar Questions

The figure shows an isosceles triangular plate of mass $M$ and base $L$. The angle at the apex is $90^o$. The apex lies at the origin and the base is parallel to the $X$-axis. The moment of inertia of the plate about the $y$-axis is:

The ratio of the moments of inertia of two uniform rings of radii $R$ and $nR$ about an axis passing through their centers and perpendicular to their planes is $1 : 8$. What is the value of $n$?

The figure shows a uniform rod of length $L$ and mass $M$ lying along the $x$-axis with one end at the origin $O$. The locus of all points $(x, y)$ in the $xy$-plane,about which the moment of inertia of the rod is the same as that about $O$,is:

The radius of gyration of a uniform thin rod of length $L$ about an axis passing normally through its centre of mass is:

The moment of inertia $I$ of a solid sphere having fixed volume depends upon its volume $V$ as

Vedclass Test Series

Exam Paper Generator

Online Exam Module