First slide

The steps in collision

Question

A sphere of mass 0.3 kg moving with a velocity of 4 m/s collides with another sphere of mass 0.5 kg which is at rest. Assuming the collision to be elastic, their velocities after the impact are

Moderate

A

4 m/s and 0 ms^-1
B

-1 m/s and 3 m/s
C

2 m/s and 2 m/s
D

4 m/s and 8 ms^-1

Solution

$\large {v_1} = \left( {\frac{{{m_1} - {m_2}}}{{{m_1} + {m_2}}}} \right){u_1} \Rightarrow {v_1} = \left( {\frac{{ - 0.2}}{{0.8}}} \right) \times 4 = - 1m/s$
$\large {v_2} = \frac{{2{m_1}{u_1}}}{{{m_1} + {m_2}}} = \frac{{2 \times 0.3 \times 4}}{{0.8}} = 3m/s$
Alternative Solutions : -
0.3 X V₁ + 0.5 X V₂ = 0.3 X 4 + 0.5 X 0
⇒ 3 V₁+ 5 V₂ = 12 ---------- (1)
V₂ -V₁ / 4-0 = 1 ⇒ V₂ -V₁ = 4 -----------------(2)
Solving , V₁ = -1 m/s and V₂ = 3 m/s

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