m = mass of the bullet = 10 g = 10 x 10⁻³ kg = 0.01 kg (since 1 g = 10⁻³ kg)
M = mass of pendulum = 2 kg
h = height to which pendulum rises = 12 cm = 0.12 m
V = velocity of the pendulum-bullet combination after collision = ?
Using conservation of energy
kinetic energy of the combination just after collision = Potential energy gained due to raise in height of the center of mass
(0.5) (m + M) V² = (m + M) gh
V = sqrt(2gh)
inserting the values
V = sqrt(2 x 9.8 x 0.12)
V = 1.5 m/s
v = velocity of the bullet before the collision
using conservation of momentum
momentum of bullet before collision = momentum of bullet-pendulum combination after collision
m v = (m + M) V
(0.01) v = (0.01 + 2) (1.5)
v = 301.5 m/s
hence initial speed of the bullet is 301.5 m/s
