A circular platform is mounted on a frictionless vertical

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A circular platform is mounted on a frictionless vertical axle. Its radius R = 2 m and its moment of inertia about the axle is 200 kgm². It is initially at rest. A 50 kg man stands on the edge of the platform and begins to walk along the edge at the speed of 1 ms^-1 relative to the ground. Time taken by the man to complete one revolution is

1. πs
2. 3π s
  2
3. 2πs
4. π s
  2

Correct Option: C

Using conservation
L_i = 0 (Initial moment)
L_ƒ = mvR – Iω (Final moment)
According to the conservation of momentum
L_i = L_ƒ
⇒ mvR – I.ω = 0
mvR = I.ω
ω = (1/2)
(v + ωR)t = 2πR

t =		1 +	1	× 2		= 2 π × 2
			2

t = 2π sec.

3π	s
2