A mass M is suspended from a light spring. An additional mass m added displaces the spring further by a distance x. Now the combined mass will oscillate on the spring with a period :

Options

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

Answer

B

Explanation

`T=2pi sqrt(("mass")/("spring const."))`
Now `k=("Force")/("extension")("mg")/("x")`.
When total mass is `M+m`.
Then `T=2pi sqrt((M+m)/((mg)/(x)))=2pi sqrt(((M+m)x)/(mg))`.
So the correct choice is (b).