Two spheres of masses 1 kg and 2 kg are moving with velocities of 10 m/s and 5 m/s respectively in the same direction. After the collision the velocity of the lighter sphere decreases by 4 m/s. What is the coefficient of restitution?

Options

A. 0.1
B. 0.15
C. 0.2
D. 0.25

Answer

C

Explanation

When the ball falls through a distance`h_(1)`, the velocity acquired by it is given vy
`v = sqrt( 2 gh_(1))` `[ :' v^(2) = u^(2) + 2gh ]`
After striking the horizontal surface, it moves upwards with a velocity v' and rises through a height `h_(2)`.
For the upwards journey,
`0 - v'^(2) - 2gh_(2)` `:. v^(1) = sqrt( 2gh_(2))`
`:.` Coefficient of restitution,
`e = ( v^(1))/( v) = sqrt((2gh_(2))/( 2gh_(1)))= sqrt((h_(2))/( h_(1)))`
`:. e = sqrt((1.28)/( 2))= sqrt( 0.64) =0.8`