Question

A disc of radius R and thickness `"R"/6` has moment of inertia/about an axis passing through its centre and perpendicular to its plane. Disc is melted and recast into a solid sphere. The moment of inertia of a sphere about its diameter is ______.

Options

• `"l"/5`

• `"l"/6`

• `"l"/32`

• `"l"/64`

Answer 1

A disc of radius R and thickness `"R"/6` has moment of inertia/about an axis passing through its centre and perpendicular to its plane. Disc is melted and recast into a solid sphere. The moment of inertia of a sphere about its diameter is `underlinebb("l"/5)`.

Explanation:

M.O.I. of disc I = `"MR"^2/2`

Volume remains constant when the disc melts into a solid sphere.

∴ Volume of disc = Volume of solid sphere

`pi"R"^2xx"R"/3=4/3pi"r"^3`

⇒ r³ = `"R"^3/8`

⇒ r = `"R"/2`

M.O.I. of solid sphere `2/5`mr² 

= `2/5xx"m"xx"R"^2/4`

= `"mR"^2/10`

= `"I"/5`

[I = moment of inertia of disc = `"MR"^2/2`]