A bit of mud stuck to a bicycle's front wheel of radius r detaches and is flung horizontally forward when it is at the top of the wheel. The bicycle is moving forward at a speed v and it is rolling without slipping. The horizontal distance travelled by the mud after detaching from the wheel is:

Options

A. `sqrt((2 r v^(2))/(g))`
B. `sqrt((8rv^(2))/(g))`
C. `sqrt(4rv^(2))/(g)`
D. `sqrt((16rv^(2))/(g))`

Answer

D

Explanation

Velocity with which mud is detached at topmost point is
`v' = v + r omega = 2v`
`d = 2v xx t`
[where `t rarr` time of fight]
`rArr d = 2v xx sqrt((4r)/(g))`
`rArr d = sqrt((16rv^(2))/(g)`