In the situation as shown in figure time period of small vertical oscillation of block will be - (String, springs and pulley are ideal)

Options

A. `2picosthetasqrt(m/(2k))`
B. `2picosthetasqrt(m/(2k))`
C. `2pisinthetasqrt(m/(2k))`
D. `2picosecthetasqrt(m/(2k))`

Answer

B

Explanation

Let block displaced through a small displacement `x` in downward direction and eleongation in spring `=x_(1)` then
Restoring force `F=2kx_(1)costheta`
`F=2kcos^(2)thetax`
Hence `T=2pisqrt(m/(2kcos^(2)theta))=2pisecthetasqrt(m/(2k))`