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Question

# A man of mass 50 kg is standing on a platform of mass 200 kg kept on a smooth horizontal surface. The man starts moving on the platform with a velocity 20 km/hr relative to the platform. Find the recoil speed of the platform.

A
4 km/hr
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B
2 km/hr
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C
3 km/hr
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D
1 km/hr
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Solution

## The correct option is A 4 km/hr Mass of man, mm=50 kg Mass of platform, mp=200 kg Initially, both man and platform are stationary. ∴vcom=0 As there is no external force in horizontal direction, acom=0 ⇒vcom will remain same (zero) even after man starts moving. After man starts moving, Given: velocity of man w.r.t platform is vm/p=20 km/hr. Let recoil velocity of platform w.r.t ground be vp and velocity of man w.r.t ground be vm. ⇒vm=vm/p+(−vp)=20 km/hr−vp vcom=0, ⇒mmvm+mp(−vp)mm+mp=0 ⇒50(20−vp)−200vp=0 ⇒vp=4 km/hr ∴ Recoil speed of platform=4 km/hr

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