`A` mass `M` is suspended from a light spring. An additional mass `m` added to it displaces the spring further by distance `x` then its time period is

Options

A. `T=((pi)/(2))sqrt(((mg)/(x(M+m))))`
B. `T=2pisqrt((((M+m))/(mgx)))`
C. `T=2pi sqrt(((mg)/(x(M+m))))`
D. `T=2pi sqrt((((M+m)x)/(mg)))`

Answer

D

Explanation

The weight mg produces a displacemtn x.
`therefore ` Spring constant `K=(F)/(x)=(mg)/(x)`
and `T=2pi sqrt(((M+m))/(K)) therefore T=2pi sqrt(((M+m)x)/(mg)`