Question

A moving mass of 8 kg collides elastically with a stationary mass of 2 kg. If E be the initial kinetic
energy of the mass, the kinetic energy left with it after collision will be
(a) 0.80 E
(b) 0.64 E
(c) 0.36 E
(d) 0.08 E​

Answer 1

answer : option (c) 0.36E

explanation : Let v1' is final speed of mass 8kg and v2' is final speed of mass 2kg.

initially, mass of 2kg is in rest so, v2 = 0

Initial kinetic energy = 1/2 (8kg)v1²

or, E = 4v1²

or, v1 = √E/2

using formula,

v2' = 2m1/(m1 + m2)v1 - (m1 - m2)/(m1 + m2)v2

= 2 × 8 /(8 + 2) × √E/2

= 8√E/10

v1' = (m1 - m2)/(m1 + m2) v1 + 2m2/(m1 + m2) v2

= (8 - 2)/(8 + 2) × √E/2 + 0

= 3√E/10

now, final kinetic energy of mass 8kg, E' = 1/2 (8kg) × (3√E/10)²

= 4 × 9E/100

= 36E/100

= 0.36 E

hence, kinetic energy left with it after collision is 0.36E

Answer 2

Answer:

$0.36e$

Hope it will help u