A bob of mass m is connected to a spring of spring constant k and a string which is fixed to the ceiling as shown in figure. Original length of the spring is L and the bob rotates in a horizontal circle centred at the fixed rod. Assuming the spring remains horizontal, then elongation in the spring is :

Options

A. `((mg - m omega^(2)L) tan theta)/(momega^(2) + k)`
B. `(mg tan theta + m omega^(2)L)/(m omega^(2) - k)`
C. `(mg tan theta + m omega^(2) L)/(k)`
D. `(g tan theta - omega^(2) L)/(omega^(2) - k//m)`

Answer

D

Explanation

`T cos theta = mg` … (i)
`T = sin theta + kx = mw^(2) (L + x)` .. (2)
from (1) and (2)
`x = (g tan theta - omega^(2)L)/(omega^(2) - (k)/(m))`