Two bodies (M) and (N) of equal masses are suspended from two separate massless springs of spring constants (k_1) and (k_2) respectively. If the two bodies oscillate vertically such that their maximum velocities are equal, the ratio of the amplitude of vibration of (M) to the of (N) is.

Options

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

Answer

D

Explanation

Maximum velocity`=a omega = asqrt((k)/(m))`
Given that `omega = sqrt((k_(1))/(m)) = a_(2)sqrt((k_(1))/(m))rArr (a_(1))/(a_(2)) = sqrt((k_(2))/(k_(1)))`