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A body is executing S.H.M. when its disp...

A body is executing S.H.M. when its displacement from the mean position is 4 cm and 5 cm, the corresponding velocity of the body is 10 cm/sec and 8 cm/sec. Then the time period of the body is

A

`2pi sec`

B

`pi//2sec`

C

`pi sec`

D

`3pi//2 sec`

Text Solution

Verified by Experts

The correct Answer is:
C
`v=omegasqrt(A^(2)-x^(2)) Rightarrow 10=omegasqrt(A^(2)-4^(2))`
`Rightarrow 8=omegasqrt(A^(2)-5^(2)) Rightarrow ((10)/(8))^(2)=(A^(2)-4^(2))/(A^(2)-5^(2)) Rightarrow (25)/(16)=(A^(2)-16)/(A^(2)-25)`
`25A^(2)-625=16a^(2)-256 Rightarrow 9A^(2)=625-256=369 Rightarrow A^(2)=(369)/(9)` `omega=(8)/(sqrt((369)/(9))-25)=(8xx3)/(sqrt369-225)=(8xx3)(12)=2 Rightarrow T=(2pi)/(omega)=pis`.
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