A block of mass m compresses a spring iof stifffness k through a distacne `l//2` as shown in the figure .If the block is not fixed to the spring the period of motion of the block is

Options

A. (a)`2pisqrt(m)/(k)`
B. (b)`(pi+4)sqrt(m)/(k)`
C. (c)`(1+pi)sqrt(m)/(k)`
D. (d)None of these

Answer

B

Explanation

`(1)/(2)k((I)/(2))^(2)=(1)/(2)mv^(2)`.`V=sqrt((k)/(m)) (I)/(2)`, `T=(2I)/(V)+(1)/(2)(2pisqrt((m)/(k)))=(4+pi)sqrt((m)/(k))`