A sphere of mass M₁, moving with a velocity v₀ collides head on with a stationary sphere of mass M₂. The collision is elastic. V₁ and V₂ are respectively their velocities immediately after collision.

List - I List - II

a) M₁ = M₂ e) V₁ = – V₀, V₂ = 0

b) M₁ << M₂ f) V₁ = 0, V₂ = V₀

c) M₁ >> M₂ g) V₀ < V₂< 2V₀

d) 2M₁> M₁+M₂ h) V₁ = V₀, V₂ = 2V₀

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a-g, b-e, c-h, d-f

a-f, b-h, c-e, d-g

a-f, b-e, c-h, d-g

a-e, b-f, c-h, d-g

answer is C.

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Detailed Solution

$M_{1} V_{1} + M_{2} V_{2} = M_{1} V_{0} \dots \dots \dots (1)$

$\frac{V_{2} - V_{1}}{V_{0} - 0} = e = 1 \dots \dots \dots (2)$

$V_{1} = (\frac{M_{1} - M_{2}}{M_{1} + M_{2}}) V_{0}; V_{2} = (\frac{2 M_{1}}{M_{1} + M_{2}}) V_{0}$

Solving,
For M₁ = M₂, V₁ = 0, V₂= V₀
For M₁ << M₂, V₁ =-V₀, V₂ $\approx$ 0
For M₁ >> M₂, V₁ =V₀, V₂= 2V₀
For 2M₁ > M₁ + M₂, V₂ > V₀

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List - I	List - II
a) M₁ = M₂	e) V₁ = – V₀, V₂ = 0
b) M₁ << M₂	f) V₁ = 0, V₂ = V₀
c) M₁ >> M₂	g) V₀ < V₂< 2V₀
d) 2M₁> M₁+M₂	h) V₁ = V₀, V₂ = 2V₀