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

$A$ cylinder of mass $500 \ g$ and radius $10 \ cm$ has a moment of inertia about an axis passing through its centre and parallel to its length equal to:

Point masses $1, 2, 3$ and $4 \text{ kg}$ are lying at the points $(0,0,0), (2,0,0), (0,3,0)$ and $(-2,-2,0)$ respectively. The moment of inertia of this system about the $x$-axis will be:

$A$ solid square plate is spun around different axes with the same angular speed. In which of the following choices of axis of rotation will the kinetic energy of the plate be the largest?

$A$ circular disc is to be made by using iron and aluminium,so that it acquires a large moment of inertia about its geometrical axis. This is possible with:

Two discs have densities $d_1 = 7.2 \ g/cm^3$ and $d_2 = 8.9 \ g/cm^3$. Both discs have the same mass and the same thickness. Find the ratio of their moments of inertia.

Vedclass Test Series

Exam Paper Generator

Online Exam Module