Question

A ring-1 oscillate with period T- about the tangential axis in the plane of ring and an another ring-2 oscillate with penod Tz about tangential axis perpendicular to plane of ring T1/T2 = ?

Answer 1

Explanation:

please refer to the attached file

Answer 2

A ring - 1 oscillates with time period T₁ about tangential axis in the plane of ring and an another ring - 2 oscillates with period T₂ about tangential axis perpendicular to plane of ring.

To find : The ratio of time period of first ring to 2nd ring.

solution : time period of oscillating Lamina is given by, T = 2π√{l/mgr}

where I is moment of inertia , m is mass , g is acceleration due to gravity and r is position of centre of mass

here T ∝ √I

so T₁/T₂ = √(I₁/I₂)

moment of inertia of ring 1, I₁ = 3/2 mR²

moment of inertia of ring 2, I₂ = 2mR²

T₁/T₂ = √(I₁/I₂) = √(3/2 mR²/2mR²) = √(3/4)

Therefore the correct option is (1)