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A cube made of wood having specific grav...

A cube made of wood having specific gravity `0.4` and side length a is floated in a large tank full of water.
If the cube is depressed slightly, it excutes SHM from It's position. What is it's time period?

A

`2pisqrt(a/g)`

B

`2pi sqrt((5a)/(2g))`

C

`2pi sqrt((2a)/(5g))`

D

`(4pi)/5sqrt(a/g)`

Text Solution

Verified by Experts

The correct Answer is:
C
`mg=F_(b)`
`a^(3)xx0.4rhog=a^(2)hrhog`
`h=2/5a`
`m=a^(3)xx0.4rho`
`F_(net)=a^(2)xrhog`
`T=2pi sqrt((a^(3)xx0.4rho)/(a^(2)rhog))`
`T=2pisqrt((2a)/(5g))`
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