Question

A wheel is subjected to uniform angular acceleration about its axis. Initially its angular velocity is zero. In the first two second it rotate through an angle θ₁, in the next 2 sec. it rotates through an angle θ_2, find the ratio (θ₂ / θ₁) = ____ 

(A) 1 

(B) 2 

(C) 3 

(D) 4

Answer 1

Correct option: (C) 3

Explanation:

θ = ω₀t + (1/2)αt² 

given ω₀ = 0

θ = (1/2)αt² 

θ = (1/2)α(2)² = 2α and

θ₁ + θ₂ = (1/2)α (2 + 2)² = 8α

i.e. θ₂ = 8α – θ₁ 

θ₂ = 6α

hence (θ₁ / θ₂) = (6α / 2α) = 3