Two bodies A and B whose masses are in the ratio `1:2` are suspended from two separate massless springs of force constants `k_(A) and k_(B)` respectively. If the two bodies oscillate vertically such that their maximum velocities are in the ratio `1:2` the ratio of the amplitude A to that of B is :

Options

A. `sqrt((k_(B))/(2k_(A)))`
B. `sqrt((k_(B))/(8k_(A)))`
C. `sqrt((2k_(B))/(k_(A)))`
D. `sqrt((8k_(B))/(k_(A)))`

Answer

B

Explanation

`v_(A)=:v_(B)=1:2`
Amplitude of A : Amplitude of `B=sqrt(K_(B)), sqrt(8K_(A))`