In the previous problem , mass of the ball is `10 g` and it is moving with `4 m//s`. The surface from the block to free end of spring is rough with friction coefficient `mu = 1//14` and of length `10 cm`. The maximum compression of spring `(k = 50 N//m)` is

Options

A. `1 cm`
B. `2 cm`
C. `3 cm`
D. `4 cm`

Answer

B

Explanation

As in the previous problem , the combined velocity
`v = (v_(0))/(4) = (4)/(1) = 1 m//s`
Velocity of combined mass after traveling `10 cm`
`v_(1)^(2) = v^(2) - 2 ad = (1)^(2) - 2 mu gd`
`= (1)^(2) - 2 xx (1)/(4) xx 10 xx (10)/(100) = (1)/(2)`
Let the maximum compression of spring be `x_(0)`,
`(1)/(2) ( m + 3m) v_(1)^(2) = (1)/(2) k x_(0)^(2)`
`(40)/(1000) xx (1)/(2) = 50 x_(0)^(2)`
`x_(0) = (1)/(50) m = 2 cm`