The moment of inertia and mass of hollow sphere and solid sphere is equal then what is ratio between their radius?

Question

The moment of inertia and mass of hollow sphere and solid sphere is equal then what is ratio between their radius? (A) 1: 2 (B)  √3:√5  (C)  √5:√3  (D) 5: 4

Tardigrade Admin · Accepted Answer

For solid sphere, moment of inertia I1=(2/5)MR12 For hollow sphere I2=(2/3)MR22 Taking, I1=I2 (R1/R2)=√(5/3)=√5:√3

Q. The moment of inertia and mass of hollow sphere and solid sphere is equal then what is ratio between their radius?

1 : 2

$3 : 5$

$5 : 3$

5 : 4

For solid sphere, moment of inertia $I_{1} = \frac{2}{5} M R_{1}^{2}$ For hollow sphere $I_{2} = \frac{2}{3} M R_{2}^{2}$ Taking, $I_{1} = I_{2}$ $\frac{R _{1}}{R _{2}} = \frac{5}{3} = 5 : 3$

Q. The moment of inertia and mass of hollow sphere and solid sphere is equal then what is ratio between their radius?

1 : 2

3​:5​

5​:3​

5 : 4

For solid sphere, moment of inertia I1​=52​MR1​2 For hollow sphere I2​=32​MR2​2 Taking, I1​=I2​ R2​R1​​=35​​=5​:3​

$3 : 5$

$5 : 3$

For solid sphere, moment of inertia $I_{1} = \frac{2}{5} M R_{1}^{2}$ For hollow sphere $I_{2} = \frac{2}{3} M R_{2}^{2}$ Taking, $I_{1} = I_{2}$ $\frac{R _{1}}{R _{2}} = \frac{5}{3} = 5 : 3$