A particle of mass `m` makes a head-on elastic collision with a particle of mass `2m` initially at rest. The velocity of the first particle before and after collision are given to be `u_(1)` and `v_(1)`. Then which of the following statements is true in respect of this collision?

Options

A. For all values of `u_(1), v_(1)` will always be less than `u_(1)` in magnitude and `|v_(1)|=(u_(1))/3`
B. The fractional loss in kinetic energy of the first particle is `8/9`
C. The gain in kinetic energy of the second particle is `8/9th` of the initial kinetic energy of the first particle
D. There is a net loss in the energy of the two

Answer

A, B, C

Explanation

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Spring can be in the state of extension, compression, or natural length in equilibrium.