A girl ridding a bicycle along a straight road with a speed of `5 ms^(-1)` throws a stone of mass 0.5 kg which has a speed of `15ms^(-1)` with respect to the ground along her direction of motion. The mass of the girl and bicycle is ` 5 kg` . Does the speed of the bicycle change after the stone is thrown ? What is the change in speed, if so ?

Options

A. `0.5 m//s`
B. `0.1m//s`
C. `0.3m//s`
D. `0.8m//s`

Answer

B

Explanation

Given total mass of girl bicycle and stone
`m_(1) = (50 + 0.5) kg =50.5kg`
Velocity of bicycle `u_(1) =5m//s`, Mass of girl and bicycle ` m = 50 kg`
Yes the speed of the bicycle changes after the stone is thrown.
Let after throwing the stone the speed of bicycle be m//s According to law of conservation of linear momentum,
`m_(1) u_(1) =m_(2) u_(2) +mv`
`50.5xx5 =0.5 xx 15 + 50 +v`
`252.5 -7.5 = 50v`
or `v = (245.0)/(50)`
`v = 4.9m//s` .