A ball impinges directly on a similar ball at rest. The first ball is brought to rest by the impact. If half of the kinetic energy is lost by the impact, the value of the coefficient of restitution is

Question

A ball impinges directly on a similar ball at rest. The first ball is brought to rest by the impact. If half of the kinetic energy is lost by the impact, the value of the coefficient of restitution is, 1 2 2, 1 3, 1 2, 3 2

MARKS App · Accepted Answer

Let u 1 and v 1 be the initial and final velocities for ball 1 and u 2 and v 2 be the initial and final velocities for ball 2 . Here, u 2 = 0 and v 1 = 0 . K i = 1 2 mu 1 2 + 1 2 mu 2 2 = 1 2 mu 1 2 K f = 1 2 mv 1 2 + 1 2 mv 2 2 = 1 2 mv 2 2 Loss of K.E = 1 2 mu 1 2 - 1 2 mv 2 2 According to question, 1 2 1 2 mu 1 2 = 1 2 mu 1 2 - 1 2 mv 2 2 (as half of K . E . is lost by the impact) ∴ u 1 2 = 2 v 2 2 or v 2 = u 1 2 ∴ e ⁡ = v 2 - v 1 u 1 - u 2 = v 2 u 1 = 1 2

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