Two trolleys of mass `m` and `3 m` are attached by a spring. The spring was compressed and then released , they move off in opposite direction and comes to rest after covering distances `s_(1)` and `s_(2)` respectively. Assuming the coefficient of friction to be uniform , the ratio of distances `s_(1) : s_(2)` is

Options

A. `1 : 9`
B. `1 : 3`
C. `3 : 1`
D. `9 : 1`

Answer

D

Explanation

`mv_(1) = 3 mv_(2) rArr v_(1) = 3v_(2)`
Distance traveled by `m` ,
`0 = v_(1)^(2) - 2 mu g s_(1)` (i)
Distance traveled by `3 m` ,
`0 = v_(2)^(2) - 2 mu gs_(2)` (ii)
`(s_(1))/(s_(2)) = ((v_(1))/(v_(2)))^(2) = (3)^(2) = 9`