Question

A disc of circumference s is at rest at a point A on a horizontal surface when a constant horizontal force begins to act on its centre. Between A and B there is sufficient friction to prevent slipping, and the surface is smooth to the right of B. AB = s. The disc moves from A to B in time T. To the right of B,

(a) the angular acceleration of the disc will disappear, linear acceleration will remain unchanged 

(b) linear acceleration of the disc will increase 

(c) the disc will make one rotation in time T/ 2 

(d) the disc will cover a distance greater than s in a further time T

Answer 1

Correct Answer is: (b. c, & d)

Let P = external force F = force of friction between A and B.

a₁ = acceleration between A and B, a₂ = acceleration beyond B.

P - F = ma₁ and P = ma_2. ∴ a₂ > a₁.

Let α = angular acceleration between A and B. For one rotation,

θ = 2π = 1/2 αT²

or T = (4π/α)^1/2 = time of travel from A to B.

Angular velocity at B = ω_B = αT.

For one rotation to the right of B,

θ = 2π = ω_Bt  or  t = 2π/αT = 1/2T²/T = T/2.