Question

A thin uniform circular disc of mass M and radius R is rotating in a horizontal plane about an axis passing through its centre and perpendicular to its plane with an angular velocity ω. Another disc of same dimensions, but of mass `1/4`M is placed gently on the first disc co-axially. The. angular velocity of the system is ______.

Options

• `2/3`ω

• `4/5`ω

• `3/4`ω

• `1/3`ω

Answer 1

A thin uniform circular disc of mass M and radius R is rotating in a horizontal plane about an axis passing through its centre and perpendicular to its plane with an angular velocity ω. Another disc of same dimensions, but of mass `1/4`M is placed gently on the first disc co-axially. The. angular velocity of the system is `underlinebb(4/5ω)`.

Explanation:

∴ I₁ = `"MR"^2/2` and I₂ = `"MR"^2/2+1/2("M"/4)"R"^2=5/8"MR"^2` 

By conservation of angular momentum,

Iω₁ = I₂ω₂ ⇒ ω₂ = `"I"_1/"I"_2`ω₁

= `((1//2)"MR"^2)/((5//8)"MR"^2)`ω

⇒ ω₂ = `4/5`ω