Two spheres of equal mass collide with the collision being absolutely elastic but not central. Then the angle between the velocities (θ) must be

Question

Two spheres of equal mass collide with the collision being absolutely elastic but not central. Then the angle between the velocities (θ) must be (A) θ= 180° (B) θ le180° (C) 90° leθ le180° (D) θ = 90°

Tardigrade Admin · Accepted Answer

Since the given collision is elastic, so we can use both. The principles of conservation of linear momentum and conservation of kinetic energy. And as the mass of the two bodies are equal and considering one body to be initially at rest, we have

u_{1} = v_{1} cos θ_{1} + v_{2} cos θ_{2} \dots

(i)

v_{1} sin θ_{1} = v_{2} sin θ_{2}

\Rightarrow v_{1} sin θ_{1} - v_{2} sin θ_{2} = 0 \dots

(ii)

u_{1}^{2} = v_{1}^{2} + v_{2}^{2} \dots

(iii)
Squaring and adding (i) and (ii), we have

v_{1}^{2} + v_{2}^{2} + 2 v_{1} v_{2} (cos θ_{1} cos θ_{2} - sin θ_{1} sin θ_{2}) = u_{1}^{2}

\Rightarrow cos (θ_{1} + θ_{2}) = 0

using (iii)

\Rightarrow cos θ = 0

where

θ = θ_{1} + θ_{2}

\Rightarrow θ^{\circ} = 90

Q. Two spheres of equal mass collide with the collision being absolutely elastic but not central. Then the angle between the velocities ( $θ$ ) must be

$θ = 18 0^{\circ}$

$θ \leq 18 0^{\circ}$

$9 0^{\circ} \leq θ \leq 18 0^{\circ}$

$θ = 9 0^{\circ}$

Q. Two spheres of equal mass collide with the collision being absolutely elastic but not central. Then the angle between the velocities (θ) must be

θ=180∘

θ≤180∘

90∘≤θ≤180∘

θ=90∘

Q. Two spheres of equal mass collide with the collision being absolutely elastic but not central. Then the angle between the velocities ( $θ$ ) must be

$θ = 18 0^{\circ}$

$θ \leq 18 0^{\circ}$

$9 0^{\circ} \leq θ \leq 18 0^{\circ}$

$θ = 9 0^{\circ}$