Centre of Mass and Collision Part 1

Given, mass of bullet (mb)=10g =10×10−3kg
Initial speed of bullet is v .
Length of pendulum, I =0.5m
Mass of bob, m=1kg
Initial speed of bob, u=0
Final speed of bullet, vb=100ms−1
Final speed of bob for making complete circle at bottom, v′=√5gl
Acceleration due to gravity, g=10ms−2
By using law of conservation of momentum
‌mbub+mu‌‌=−mbvb+mv′
⇒‌‌

10

1000

v+0‌‌=‌

−10

1000

×100+1√5gl
⇒‌‌

v

100

‌‌=−1+√5×10×‌

5

10

⇒‌‌

v

100

‌‌=−1+5
⇒‌v‌‌=4×100=400ms−1