A system of two blocks `A` and `B` are connected by an inextensible massless string as shown in Fig. The pulley is massless and frictionless. Initially, the system is at rest. A bullet of mass `'m'` moving with a velocity `'u'` as shown hits block If and gets embedded into it. The impulse imparted by tension force to the block of mass `3m` is

Explanation

Let velocity of B and A after collision has magnitude v. At the time of collision tension = T
Impulse provided by tension `= int T dt`
For bullet
`- int Fdt = mv - mu " "` …(1)
For block B
`int (F-T)dt = mv " "` ....(2)
Consider change of momentum of (B + bullet)
`mu - int Tdt = 2mv " "` ....(i)
Consider change of momentum A
`int T dt = 3 mv " "` ....(ii)
from (i) and (ii)
mu = 5 mv
v = u/5
Hence, Impulse `int Tdt = 3mv = 3m((u)/(5))=(3mu)/(5)`