Question

A block of mass 'M' is suspended from one end of a spring of force constant 'k'. The other end is rigidly attached to a horizontal platform. The mass oscillates vertically with a time period 'T'. If the mass gets detached from the spring, then the length of the spring will be shortened by (g = acceleration due to gravity).

Options

• `"gT"^2/(2pi^2)`

• `"gT"^2/(2pi)`

• `"gT"^2/(4pi)`

• `"gT"^2/(4pi^2)`

Answer 1

`"gT"^2/(4pi^2)`

Explanation:

Time period T = `2pi sqrt("m"/"k")`

`=> "T"^2 = 4pi^2 "m"/"k"`

`=> "k" = (4pi^2 "m")/"T"^2`

mg = kx

`therefore x = "mg"/"k" = "mg" "T"^2/(4pi^2 "m") = "gT"^2/(4pi^2)`