A body of mass m1 moving at a constant speed undergoes an elastic collision with a body of mass m2 initially at rest. The ratio of the kinetic energy of mass m1 after the collision to that before the collision is
A
(m1−m2m1+m2)2
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B
(m1+m2m1−m2)2
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C
(2m1m1+m2)2
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D
(2m2m1+m2)2
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Solution
The correct option is A(m1−m2m1+m2)2 Let u1 be the speed of mass m1 before the collision.
Here u2=0. Therefore, the speeds of masses m1 and m2 after the collision respectively are v1=(m1−m2m1+m2)u1
and v2=(2m1m1+m2)u1 ∴ KE of m1 after collision = 12m1v21=12m1(m1−m2m1+m2)2u21. KE of m1 before collision = 12m1u21.
The ratio of the two is (m1−m2m1+m2)2. Hence the correct choice is (a)