Two identical springs are fixed at one end and masses `1kg` and `4kg` are suspended at their other ends. They are both strethced down form their mean position and let go simultaneously. If they are in the same phase after every `4` seconds then the springs constant `k` is

Options

A. (a)`pi`
B. (b)`pi^(2)`
C. (c)`2pi`
D. (d)given data is insufficient

Answer

B

Explanation

`omega_(1) = sqrt((k)/(m)), omega_(2) = sqrt((k)/(4m)) = (omega_(1))/(2)`
`(omega_(1) - omega_(2)) t = 0, 2pi, 4pi,"……" t = 0`
`rArr t = (2pi)/(omega_(1) - omega_(2)) = 4 rArr 2pi = 4 (omega_(1) - omega_(2))`
`rArr (pi)/(2) = (omega_(1) - omega_(2)) rArr k = pi^(2)N//m`