A lump of clay whose rest mass is 4 kg is travelling at three-fifths the speed of light when it collides head-on with an identical lump going the opposite direction at the same speed. If the two lumps stick together and no energy is radiated away, what is the mass of the composite lump?

mass of the composite lump is 10 kg

Explanation:

given data

mass = 4 kg

to find out

mass of composite lump

solution

we know energy is conserved so

so m1 = m2 = m0 that is 4kg

and

E (1) release + E (2) release = E (1,2) rest

so γ (1) m (1) c² + γ (2) m (2) c² = Mc² ... 1

that why here

|v (1) | = |v (2) | = 3/5 c ... 2

and

γ = 1 / √ (1 - v²/c²) ... 3

put here v = 3 and c is 5

γ = 1 / √ (1 - 9/25)

γ = 5/4

so

γ (1) = γ (2) = γ = 5/4

so from equation 1

γ (1) m (1) c² + γ (2) m (2) c² = Mc²

M = 2γm0

M = 2 (5/4) (4)

M = 10 kg

so mass of the composite lump is 10 kg