Two springs fixed at one end are stretched by 4 cm and 12 cm, respectively, when masses of 0.5 kg and 1 kg are suspended at their lower ends. They are displaced slightly from their mean positions and released. What is the ratio of their periods of oscillation ?

Options

A. `1 : sqrt(2)`
B. `1 : 2`
C. `1 : sqrt(3)`
D. `2 :5`

Answer

C

Explanation

For a loaded spring of spring constant K and extension x,
`K=(F)/(x)=(mg)/(x)`
`therefore T=2pi sqrt((m)/(K))=2pi sqrt((mx)/(mg))=2pi sqrt((x)/(g))`
`therefore (T_(1))/(T_(2))=sqrt((x_(1))/(x_(2))=sqrt((4)/(12))=(1)/(sqrt(3))`