A body of mass `m` is attached by an inelastic string to a suspended spring of spring constant `k`. Both the string and the spring have negligible mass and the string is inextensible and of length `L`. Initially, the mass `m` is at rest.
The largest amplitude `A_(max)`, for which the string will remain taut throughout the motion is

Options

A. `(mg)/(2k)`
B. `(mg)/(k)`
C. `L//2`
D. `L`

Answer

B

Explanation

In equilibrium extension in the strig is `x_(0) = (mg)/(k)`. For the string will remain taut in the motion maximum `= x_(0) = (mg)/(k)`