A girl riding 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 15 `ms^(-1)` with respect to the ground along her direction of motion. The mass of the girl and bicycle is 50 kg. Does the speed of the bicycle change after the stone is thrown ? What is the change in speed, if so

Options

A. `2.0 ms^-1`
B. `0.1 ms^-1`
C. `0.5 ms^-1`
D. `5.2 ms^-1`

Answer

B

Explanation

initial speed of girl, cycle and stone,
`u=5ms^-1`
Final speed of stone `v_1=15 ms^-1`
Final speed of cycle with girl `v_2`=?
Mass of cycle with girl M=50 kg
Mass of stone m=0.5 kg
Initial momentum of the system
`P_i=(50+0.5) times 5=252.5 kg ms^-1`
Final momentum of the system
`P_f=50 v_2+0.5 times 15= (50v_2+7.5) kg ms^-1`
From law of conservation of momentum
`P_f=P_i implies 50v_2+7.5 -252.5 implies 50v_2=245`
`implies v_2=245/50=4.9 ms^-1`
change in speed `=5-4.9=0.1 ms^-1`