A wheel initially at rest, begins to rotate about its axis with constant angular acceleration. If it rotates through an angle ₁ in first 2 s and a further angle ₂ in the next 2 s , the ratio ₁: ₂ is

Step-by-step solution

For a wheel rotating with constant angular acceleration α starting from rest, the angular displacement follows θ = (1/2)αt 2 . During the first 2 seconds: θ 1 = (1/2)α(2) 2 = 2α During the first 4 seconds: θ total = (1/2)α(4) 2 = 8α The angular displacement during the subsequent 2 seconds is therefore θ 2 = θ total - θ 1 = 8α - 2α = 6α The ratio θ 1 : θ 2 evaluates to 2α : 6α = 1 : 3 . Final answer: D