A man of mass `50 kg` is runing on a plank of mass `150 kg` with speed of `8 m//s` relative to plank as shows in the figure (both were initially at rest and velocity of man with respect to ground any how remains constant). Plank is placed on smooth horizontal surface. The man, while running, whistle with frequency `f_(o)`. `A` detected `(D)` placed on plank detects frequency. The man jumps off with same velocity (w.r.t. to ground) from point `D` and slides on the smooth horizontal surface [Assume coefficient of friction between man and horizontal is zero]. The speed of sound in still medium is `330 m//s`. Answer the following questions on the basis of above situations.

The frequency of sound detected by detector `D`, before man jumps of the plank is

Options

A. `(332)/(324) f_(o)`
B. `(330)/(322) f_(o)`
C. `(328)/(336) f_(o)`
D. `(330)/(338) f_(o)`

Answer

A

Explanation

`O_underset(Plank)(rarr v)` `8-v_underset(Man)(larr)S`
From conservation of linear momentum,
`50 (8 - nu) = 150nu`
:. `nu = 2 m//s`
`8 - nu = 6 m//s`
`f_(1) = f_(o) ((nu + nu_(o))/(nu - nu_(s)))`
`= f_(o) ((330 + 2)/(330 - 6)) = (332)/(324) f_(o)`