physics
posted by srikala .
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?

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

yes the bob goes straight up and stops

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