A block B is pushed momentarily along a horizontal surface with an initial velocity V. If mu is the coefficient of sliding friction between B and the surface, block B will come to rest after a time ?

Options

A. `(g mu)/(v)`
B. `(g )/(v)`
C. `(v)/(g)`
D. `(v)/(g mu)`

Answer

D

Explanation

Initial velocity of a block = `v_(0) = v`
Final velocity v= 0
Now v= `v_(0) + at`
`0 = v - at`
`a= (0-v)/(t ) =- (v )/(l )`
Now friction force f= `mu` R = `mu` mg `(:. , R = mg ) `
`:. ,` Retardation - ma = `mu mg`
from equation (1) and (2)
`(v)/( t ) = mu g ` (Avoiding - sign)
`t= (v ) /(mu g)`