Question

A system of two block a and b are connected by an inextensible massless string . the pulley is massless and frictionless. initially system is at rest. a bullet of mass m moving with velocity u and hit block b and gets embedded into it. the impulse imparted by tension force to the block of mass 3m is

Answer 1

Let velocity of B and A after collision has magnitude v.

At the time of collision tension = T

Impulse provided by tension = ∫ Tdt

Consider change of momentum of (B + bullet)

mu – ∫ Tdt = 2mv     ……… (i)

Consider change of momentum A

∫ Tdt = 3mv     …………..(ii)

from (i) and (ii), mu = 5 mv

=> v = u/5

Hence, Impulse ∫ Tdt = 3mv

= 3m(u/5) = 3mu/5