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A system of two blocks A and B are connected by an inextensiible massless string as shown in figure. The pulley is massless and frictionless. Initially, the system is at rest. A bullet of mass m moving with a velocity u as shown in the figure hits block B and gets embedded into it. Then find out the impulse imparted by tension force to the block of mass 3m, immediately after the collision takes place.



A
54mu
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B
45mu
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C
25mu
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D
35mu
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Solution

The correct option is D 35mu
Tension in both strings will be equal, hence impulse due to tension on both blocks will be the same.
J1=J2=J (assuming ve y direction upwards)

After collision, mass of block B becomes 2m due to embedded bullet.

The system of (blocks+bullet) will move with common speed v, to satisfy string constraint. Block A moves upwards with speed v and B downwards with speed v

Applying impulse-momentum theorem on both blocks, considering vertically downwards as +ve y axis:
For block A:
J=PfPi=3m(vfvi)
=3m(v0)=3mv ...(i)
For block B:
J=PfPi=2m(v)[(m×0)+(m×u)]
=2mvmu ...(ii)

Equating Eq. (i) and (ii):
3mv=2mvmu
5mv=mu
v=u5

Hence, impulse on block A:
=J=2mvmu=25mumu
=35mu
|J|=35mu

Physics

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