Question

A hollow cylinder of mass m and radius R is kept on a rough surface after giving its centre a horizontal speed v0. The speed of centre of the cylinder when it starts pure rolling is​

Answer 1

Explanation:

Given A hollow cylinder of mass m and radius R is kept on a rough surface after giving its centre a horizontal speed v0. The speed of centre of the cylinder when it starts pure rolling is​

• Now frictional force = f = μ N
• Or N = mg
• So f = μ m g
• When it stops slipping we need to find the value of Vo
• So torque of all force about the point of contact is zero.
• So ∑τ p = 0
• So there will be translation and rotational motion.
• So translation motion will be L = mv (centre of mass) rl(perpendicular distance) + I cm (moment of inertia for centre of mass) ω

• So L = m v r + I ω
•         = m Vo R + m R^2 / 2 x 0 (moves in clockwise direction)
• Now final momentum will be
• L f = m V (cm) r (l) + I (cm) ω (it will be rolling)
•      = m v R + m R^2 / 2 ω
•      = m v R + m R^2  / 2 x v / R
•      = m v R + m v R / 2 after cancelling R
• So L f = 3/2 m v R
• Therefore initial angular momentum = final angular momentum
• Or L I = L f
• Angular momentum will be conserved
• So m Vo R = 3/2 m V R
• Therefore v = 2 Vo / 3

Reference link will be

https://brainly.in/question/7598640