- #1

Jahnavi

- 848

- 102

## Homework Statement

## Homework Equations

## The Attempt at a Solution

C is the point of contact and G is the CM of the plank . x be the distance between G and C .Since plank always remain in contact , x=aθ

When the line joining the point of contact C with the center makes an angle θ with the vertical ,the force due to gravity mg acts vertically down and exerts a torque about the point of contact C.

Torque due to Mg = Mgxcosθ

Since θ is small , cosθ ≈ 1 and using x=aθ

Mgxcosθ ≈ Mgaθ

Moment of inertia about C = M(2b)

^{2}/12 + Mx

^{2}=Mb

^{2}/3+Ma

^{2}θ

^{2}

Since θ is small , θ

^{2}≈0

Moment of inertia about C = Mb

^{2}/3

Writing torque equation about C ,

-Mgaθ = (Mb

^{2}/3)α ( α is angular acceleration )

α = -3gaθ/b

^{2}

Angular frequency of oscillation ω = √(3ga)(1/b)

Time period = 2π/ω = 2πb/√(3ga)

Is my work correct ?