A spherical shell has a mass one-fourth that | vedclass

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

Question

(B) Let the mass of the solid sphere be $M$ and its radius be $R_S$.Let the mass of the spherical shell be $M_H = \frac{M}{4}$ and its radius be $R_H$

Vedclass · Accepted Answer

$\sqrt{12} : \sqrt{5}$

Vedclass · Answer

(B) Let the mass of the solid sphere be $M$ and its radius be $R_S$.Let the mass of the spherical shell be $M_H = \frac{M}{4}$ and its radius be $R_H$.The moment of inertia of a solid sphere about its diameter is $I_{SS} = \frac{2}{5} M R_S^2$.The moment of inertia of a spherical shell about its diameter is $I_{HS} = \frac{2}{3} M_H R_H^2 = \frac{2}{3} (\frac{M}{4}) R_H^2 = \frac{1}{6} M R_H^2$.Given that $I_{HS} = I_{SS}$,we have:$\frac{1}{6} M R_H^2 = \frac{2}{5} M R_S^2$$\frac{R_H^2}{R_S^2} = \frac{2}{5} 	imes 6 = \frac{12}{5}$$\frac{R_H}{R_S} = \sqrt{\frac{12}{5}} = \frac{\sqrt{12}}{\sqrt{5}}$Thus,the ratio of their radii $R_H : R_S$ is $\sqrt{12} : \sqrt{5}$.

$A$ spherical shell has a mass one-fourth that of a solid sphere,and both have the same moment of inertia $(M.I.)$ about their respective diameters. The ratio of their radii will be:

Similar Questions

Two uniform thin identical rods $AB$ and $CD$ each of mass $M$ and length $L$ are joined so as to form a cross as shown. The moment of inertia of the cross about a bisector line $EF$ is (Line $EF$ is in the plane of the cross and bisects the angle between the rods).

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 figure shows a thin metallic triangular sheet $ABC.$ The mass of the sheet is $M.$ The moment of inertia of the sheet about side $AC$ is

The moment of inertia of a body depends on

The radius of gyration of a circular disc of radius $R$ and mass $m$ rotating about its diameter as an axis is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module