a pendulum consists of a wooden bob of mass m and length l. A Bullet of mass m1 is fired towards the pendulum with a speed v1.the bullet emerges out of the bob with a speed v1/3 and the bob just completes motion along a vertical line ,then v1 is?

Answer 1

What do you mean by "completes motion along a vertical line" ? Does the bob go straight up and stop?

Answer 2

yes the bob goes straight up and stops

Answer 3

Let Vf be the bob velocity just after the bullet has gone through, before it has started to swing upwards.

(1/2)Vf^2 = 2 g l
(from conservation of energy)
Vf = sqrt (4 g*l) = 2 sqrt(g*l)

Now apply conservation of momentum to the bullet interaction:
m1*v1 = m1*(v1/3) + m*Vf
(2/3)m1*v1 = 2*m*sqrt(g*l)
v1 = 3(m/m1)*sqrt(g*l)

Answer 4

What if the motion of the bob after collision just complete along a vertical circle??