A circular disc of radius R and thickness fra | vedclass

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

Question

(C) The mass of the disc and the sphere remains the same because the disc is melted and recast into a sphere.Volume of disc = Volume of sphere$\pi R^2

Vedclass · Accepted Answer

$\frac{I}{5}$

Vedclass · Answer

(C) The mass of the disc and the sphere remains the same because the disc is melted and recast into a sphere.Volume of disc = Volume of sphere$\pi R^2 t = \frac{4}{3} \pi R_s^3$Given $t = \frac{R}{6}$,so $\pi R^2 (\frac{R}{6}) = \frac{4}{3} \pi R_s^3$$\frac{R^3}{6} = \frac{4}{3} R_s^3 \implies R_s^3 = \frac{R^3}{8} \implies R_s = \frac{R}{2}$The moment of inertia of the disc is $I = \frac{1}{2} M R^2$,so $M R^2 = 2I$.The moment of inertia of the sphere about its diameter is $I_s = \frac{2}{5} M R_s^2$.Substituting $R_s = \frac{R}{2}$,we get $I_s = \frac{2}{5} M (\frac{R}{2})^2 = \frac{2}{5} M \frac{R^2}{4} = \frac{M R^2}{10}$.Since $M R^2 = 2I$,then $I_s = \frac{2I}{10} = \frac{I}{5}$.

$A$ circular disc of radius $R$ and thickness $\frac{R}{6}$ has a moment of inertia $I$ about an axis passing through its center and perpendicular to its plane. It is melted and recast into a solid sphere. The moment of inertia of this sphere about its diameter is:

Similar Questions

The integrating factor of the differential equation $x \log x \frac{dy}{dx} + y = 2 \log x$ is given by

In the circuit shown,the reading of the Ammeter is doubled after the switch is closed. Each resistor has a resistance $1\,\Omega$ and the ideal cell has an $e.m.f.$ $10\,V$. Then,the Ammeter has a coil resistance equal to ............ $\Omega$

What is the primary purpose of data entry in the context of mathematical analysis?

Explain the reason for the fusion of an organic compound with metallic sodium for testing nitrogen,sulphur and halogens.

If $g(x) = \int_0^x \cos^4 t \, dt$,then $g(x + \pi)$ equals

Vedclass Test Series

Exam Paper Generator

Online Exam Module