Question

A uniform disc of mass M and radius R rolls without slipping down a plane inclined at an angle θ with the horizontal. The acceleration of the centre of mass of the disc is 

(A) g sin θ 

(B) [(2g sin θ) / 3] 

(C) [(g sin θ) / 3] 

(D) [(2g cos θ) / 3]

Answer 1

Correct option: (B) [(2g sin θ) / 3]

Explanation:

As disc rolls down the plane, frictional force F acts up words along the plane.

Mg sinθ – f = Ma         (1)

Also τ = Iα

Τ = f ∙ R hence

f ∙ R = I ∙ α

f = [(I ∙ α) / R] = [(MR²) / 2] ∙ (α/R) = [(MRα) / 2] 

as α = (a/R)

f = [(MR ∙ a) / (R ∙ 2)] = [(Ma) / 2]            (2)

putting (2) in (1)

Mg sin θ = f + Ma = (3/2)Ma

a = [(2g sin θ) / 3]