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Question

A trolley of mass M=150 kg is at rest over a smooth horizontal surface. Two boys each of mass  m=50 kg are standing over the trolley. If they jump from the trolley with a relative velocity vr=20 m/s (relative to the velocity of trolley just after jumping) one after other in same direction. The final recoil speed of trolley is


A
6 m/s
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B
8 m/s
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C
9 m/s
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D
12 m/s
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Solution

The correct option is C 9 m/s
Let v1 be the velocity of trolley when the first boy jumps


As there are no net external force in horizontal direction.
Applying PCLM,
pi=pf
0=m(vrv1)(M+m)v1
v1=mvrM+2m   ...(i)

Now the 2nd boy jumps, let v2 be the velocity of trolley.


Again there are no external force in horizontal direction
Applying PCLM,
pi=pf
(M+m)v1=m(vrv2)Mv2
v2=(mM+m)vr+v1   (ii)
Using equation (i) and (ii)v2=mvr[1M+m+1M+2m]
=50×20[1200+1250]
=9 m/s
 

Physics

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