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Question

A man of mass 75 kg is standing on a platform of mass 15 kg kept on a smooth horizontal surface. The man starts moving on the platform with a velocity of 20 m/s relative to the platform. Then, magnitude of the recoil velocity of the platform is 
  1. 12.33 m/s
  2. 20 m/s
  3. 25 m/s
  4. 16.66 m/s


Solution

The correct option is D 16.66 m/s
Taking the platform and the man as a system, Fext=0 on the system in horizontal direction.

The linear momentum of the system remains constant and system was at rest intitially.
Pi=Pf=0 ...(i)
Mass of man (m1)=75 kg
Mass of platform (m2)=15 kg

Given, velocity of man is 20 m/s be w.r.t platform (along +ve x direction) 
Let the recoil velocity of platform be v m/s (along ve x axis). 
Velocity of man w.r.t ground is (20v) m/s
From Eq (i):
Pf=0
75(20v)+15(v)=0
90v=1500
v=150090=16.66 m/s

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