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Center of Mass and Collision question

2012 · Q156
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Center of Mass and Collision question

2012 · Q156

NEETPhysicsCenter of Mass and CollisionMCQ+4 / −1
Two spheres A and B of masses m1 and m2 respectively collide. A is at rest initially and B is moving with velocity v along x-axis. After collision B has a velocity v2{v \over 2}2v​ in a direction perpendicular to the original direction. The mass A moves after collision in the direction :
  1. A
    same as that of B
  2. B
    opposite to that of B
  3. C
    θ\thetaθ = tan−-−1 (12)\left( {{1 \over 2}} \right)(21​) to the x-axis
  4. D
    θ\thetaθ = tan−-−1(−12)\left( { - {1 \over 2}} \right)(−21​) to the x-axis
View written solutionFree

Correct answer: D

AIPMT 2012 Prelims Physics - Center of Mass and Collision Question 28 English Explanation

conservation of linear momentum along x-direction

$${m_2}v = {m_1}{v_x} \Rightarrow {{{m_2}v} \over {{m_1}}} = {v_x}$$

along y-direction

$${m_2} \times {v \over 2} = {m_1}{v_y} \Rightarrow {v_y} = {{{m_2}v} \over {2{m_1}}}$$

Note: Let A moves in the direction, which makes an angle q with initial direction i.e.

$$\tan \theta = {{{v_y}} \over {{v_x}}} = {{{m_2}v} \over {2{m_1}}}/{{{m_2}v} \over {2{m_1}}}$$

$$\tan \theta = {1 \over 2}$$

$$\tan \theta = {1 \over 2} \Rightarrow \theta = {\tan ^{ - 1}}\left( {{1 \over 2}} \right)$$ to the x-axis.
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