The moment of inertia of a solid sphere of radius R about its diameter is same as that of a disc of radius 2R about its diameter. The ratio of their masses is

Question

The moment of inertia of a solid sphere of radius R about its diameter is same as that of a disc of radius 2R about its diameter. The ratio of their masses is (A) 5:2 (B) 5:8 (C) 4:1 (D) 2:1

Tardigrade Admin · Accepted Answer

The moment of inertia of a disc of radius 2 R about its diameter I d =(1/4) M d (2 R )2 Given, I s =Id (2/5) M s R 2=(1/4) M d (2 R )2 ( M s / M d )=(5/2)

Q. The moment of inertia of a solid sphere of radius $R$ about its diameter is same as that of a disc of radius $2 R$ about its diameter. The ratio of their masses is

$5 : 2$

$5 : 8$

$4 : 1$

$2 : 1$

The moment of inertia of a disc of radius $2 R$ about its diameter
$I_{d} = \frac{1}{4} M_{d} (2 R)^{2}$
Given, $I_{s} = I_{d}$
$\frac{2}{5} M_{s} R^{2} = \frac{1}{4} M_{d} (2 R)^{2}$
$\frac{M _{s}}{M _{d}} = \frac{5}{2}$

Q. The moment of inertia of a solid sphere of radius R about its diameter is same as that of a disc of radius 2R about its diameter. The ratio of their masses is

5:2

5:8

4:1

2:1