A smooth sphere of mass m strikes a second sphere of mass 2m which is at rest. After the collision their directions of motion are at right angles. Then coefficient of restitution is-
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The correct answer is 1/2
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The value of coefficient of restitution is 1/2.
Let the sphere of mass m move towards stationary sphere of mass 2m with a velocity v.
The mass m collides with 2m at an angle x w.r.t the line joining the centers of the two spheres .
Initial momentum w.r.t to the line joining the centers of the spheres = m vcosx
Final momentum = 2m v2
According to law of conversation of momentum -
=> m vcosx = 2m v2
=> vcosx = 2v2
e = coefficient of restitution = velocity after collision / velocity before collision
= v2/vcosx
= 1/2
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