Two identical blocks `A` and `B` connected by massless string, are placed on a frictionless horizontal plane. A bullet havig the same mass, moving with speed `u` strickes block `B` from behind as shown. If the bullet gets embedded into block `B` then find

a. the velocity of `A,B,C` after collision.
b. impulse on `A` due to tension in the string,
c. impulse on `C` due to normal force of collision,
d. impulse on `B` due to normal force of collision.

Explanation

a. By a conservstion of linear momentum, `v=u//3`
b. `intTdt=("mu")/3`
`c. intNdt=m(u/3-u)=(-2"mu")/3`
(-ve sign indicates left direction)
d. `int(N-T)dt=intNdt-intTdt=("mu")/3impliesintNdt=(2"mu")/3`