First slide

Special cases

Question

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

Moderate

A

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

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

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

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

Solution

$\large {M_1}{V_1} + {M_2}{V_2} = {M_1}{V_0}.....(1)$
$\large \frac{{{V_2} - {V_1}}}{{V_0 - 0}} = e = 1.....(2)$
Solving, $\large {V_1} = \left( {\frac{{{M_1} - {M_2}}}{{{M_1} + {M_2}}}} \right){V_0};\;{V_2} = \left( {\frac{{2{M_1}}}{{{M_1} + {M_2}}}} \right){V_0}$
For M₁ = M₂, V₁ = 0, V₂= V₀
For M₁ << M₂, V₁ =-V₀, V₂ $\large \simeq$ 0
For M₁ >> M₂, V₁ =V₀, V₂= 2V₀
For 2M₁ > M₁ + M₂, V₂ > V₀

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