A block of mass `M` is kept on a smooth surface and touches the two springs as shown in the figure but not attached to the springs. Initially springs are in their natural length. Now, the block is shifted `(l_(0)//2)` from the given position in such a way that it compresses a spring and released. The time - period of oscillation of mass will be

Options

A. `(pi)/(2)sqrt((M)/(K))`
B. `2pisqrt((M)/(5K))`
C. `(3pi)/(2)sqrt((M)/(K))`
D. `pisqrt((M)/(2K))`

Answer

C

Explanation

`T=pi[sqrt((M)/(K))+(1)/(2)sqrt((M)/(K))]=(3pi)/(2)sqrt((M)/(K))`