Two bodies A and B of equal mass are suspended from two separate massless springs of spring constant `k_1 and k_2` respectively. If the bodies iscillte vertically such that their maxixum velocities are equal, the ratio of the amplitude of A to that of B is

Options

A. `sqrt((k_(1))/(k_(2)))`
B. `sqrt((k_(2))/(k_(1)))`
C. `(k_(1))/(k_(2))`
D. `(k_(2))/(k_(1))`

Answer

B

Explanation

`v_(max)=omegaA,so,omega_(A)A_(A)=omega_(B)A_(B)implies(A_(A))/(A_(B))=(omega_(B))/(omega_(A))`
`=sqrt((k_(2))/(m))+sqrt((k_(1))/(m))=sqrt((k_(2))/(k_(1)))`