Question

two identical spheres are rolling down the slope one is solid and other is hollow the ratio of moment of inertia of solid to that of hollow

Answer 1

Hello Mate,

Here is your answer,

Given:

• Solid sphere and hollow sphere are rolling down a slope.

To find:

• Ratio of moment of inertia of solid sphere to that of hollow sphere.

Formulas Used:

Moment of Inertia of solid sphere

= $\frac{2}{5} \: m {r}^{2}$

Moment of Inertia of hollow sphere

= $\frac{2}{3} \: m {r}^{2}$

Solution:

Solid sphere : Hollow sphere (ratio)

Substitute the Formulas,

$\frac{ \frac{2}{5} \: m {r}^{2} }{ \frac{2}{3} m {r}^{2} } \\ \\ = \frac{ \frac{2}{5} }{ \frac{2}{3} } \\ \\ \frac{2}{5} \times \frac{3}{2} \\ \\ = \frac{3}{5}$

= 3 : 5

The required ratio is 3 : 5

Hope it helps:)