A 7.7 kg sphere makes a perfectly inelastic collision with a second sphere initially at rest. The composite system moves with a speed equal to one third the original speed of the 7.7 kg sphere. What is the mass of the second sphere

The mass of the second sphere is 15.4 kg

Explanation:

Given;

mass of the first sphere, m₁ = 7.7 kg

initial velocity of the second sphere, u₂ = 0

let mass of the second sphere =  m₂

let the initial velocity of the first sphere = u₁

final velocity of the composite system, v = ¹/₃ x u₁ =

From the principle of conservation of linear momentum;

Total momentum before collision = Total momentum after collision

m₁u₁ + m₂u₂ = v(m₁ + m₂)

Substitute the given values;

Divide through by u₁

7.7 = ¹/₃(7.7 + m₂)

multiply both sides by 3

23.1 = 7.7 + m₂

m₂ = 23.1 - 7.7

m₂ = 15.4 kg

Therefore, the mass of the second sphere is 15.4 kg

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