A spring of force constant `k` is cut into two parts whose lengths are in the ratio `1:2`. The two parts are now connected in parallel and a block of mass `m` is suspended at the end of the combined spring. The period of oscillation of block is

Options

A. `2pi sqrt((2m)/(9K))`
B. `2pi sqrt((m)/(9K))`
C. `2pi sqrt((2m)/(5K))`
D. `2pi sqrt((m)/(5K))`

Answer

A

Explanation

`l_(1) = (l)/(2), l_(2) = (2l)/(3)`
`(K)/(K_(1)) = ((l)/(3))/(l) rArr K_(1) = 3K`
`(K)/(K_(2)) = ((2l)/(3))/(l) rArr K_(2) = (3)/(2)K`
In parallel combination
`K_(p) = K_(1) + K_(2) = 3K + (3K)/(2) = (9K)/(2)`
`T = 2pi sqrt((2m)/(9K))`