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A block of mass m compresses a spring io...

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

A

`2pisqrt(m)/(k)`

B

`(pi+4)sqrt(m)/(k)`

C

`(1+pi)sqrt(m)/(k)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
`(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))`
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