Ratio of moment of inertia of two rings is 2: 1 and ratio of their diameters is 2: 1. Then, the ratio of their mass will be

Question

Ratio of moment of inertia of two rings is 2: 1 and ratio of their diameters is 2: 1. Then, the ratio of their mass will be (A) 2: 1 (B) 1: 2 (C) 1: 4 (D) 1: 1

Tardigrade Admin · Accepted Answer

Moment of inertia of ring I=m r2 (I1/I2)=((m1/m2))((r1/r2))2 Given, (I1/I2)=(2/1) And (r1/r2)=(2/1) (2/1)=((m1/m2))((2/1))2 Hence, (m1/m2)=1: 2

Q. Ratio of moment of inertia of two rings is $2 : 1$ and ratio of their diameters is $2 : 1$ . Then, the ratio of their mass will be

2 : 1

1 : 2

1 : 4

1 : 1

Moment of inertia of ring $I = m r^{2} \frac{I _{1}}{I _{2}} = (\frac{m _{1}}{m _{2}}) (\frac{r _{1}}{r _{2}})^{2}$
Given, $\frac{I _{1}}{I _{2}} = \frac{2}{1}$
And $\frac{r _{1}}{r _{2}} = \frac{2}{1}$
$\frac{2}{1} = (\frac{m _{1}}{m _{2}}) (\frac{2}{1})^{2}$
Hence, $\frac{m _{1}}{m _{2}} = 1 : 2$

Q. Ratio of moment of inertia of two rings is 2:1 and ratio of their diameters is 2:1. Then, the ratio of their mass will be