A body of mass 5kg makes an elastic head on Collison with an object of unknown mass and moves in original direction after Collison with a velocity equal to 1/10th of the original velocity. Calculate the mass of second object

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Solution

m1 = 5 kg
u1 = u1
v1 = u1/10
m2 = ?
u2 = 0
v2 = ?

Elastic Collision => Conservation of Linear Momentum and Total Energy.

m1 u1 + m2 u2 = m1 v1 + m2 v2
substituting the values,
5 u1 + 0 = 5 u1 /10 + m2×v2
5u1=2u1+m2×v2
=> v2 = 3 u1/ m2
By energy conservation,
1/2m1u1²+1/2m2u2²=1/2m1v1²+1/2m2v2²
substituting,
1/2 ×5× u1² + 1/2 ×m2 × 0 = 1/2 ×5× u1²/100 + 1/2 ×m2 × v2²

5u1²=(1/20)u1²+m2v2²
(99/20)u1²=m2(3u1/m2)²

99/20=9/m2
m2 = 20/11 = 1.81 kg

Hence mass is 1.81 kg

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