Question

A cylinder of mass M; radius R is set into motion on a rough horizontal surface with a linear speed v₀ in forward direction and an angular speed of v₀/3R in anticlockwise direction. μ is coefficient of friction between cylinder and horizontal surface. The linear speed of cylinder when it starts rolling is

(1) v₀/2

(2) 4v₀/5

(3) 5v₀/7

(4) 7v₀/9

Answer 1

(4) 7v₀/9

Given ω₀ = v₀/3R.

Since v₀ ≠ Rω ; the cylinder slips an horizontal surface. Consider motion about an axis fixed to ground and passing through the instantaneous point of contact of cylinder with ground. There is no net torque about this axis; therefore angular momentum is conserved. Let v and ω denote the linear and angular speed when cylinder stops slipping i.e. it starts rolling. Then