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  • Consider a solid cylinder of density  and  total height h, is floating in a liquid of density&

Consider a solid cylinder of density \sigma and  total height h, is floating in a liquid of density \rho as shown below figure.And  \left( \sigma < \rho \right) .

If l is the length of cylinder dipping in liquid as shown in the above figure.

Then what is the relation between l and h

 

Option: 1

l=\frac{h}{2}


Option: 2

l= \frac{h\sigma }{\rho }


Option: 3

l= \frac{h\rho}{\sigma }


Option: 4

 h=l


Answers (1)

best_answer

 

 

Time period of floating body -

A floating body is in a stable equilibrium. When it is displaced up and released, it accelerates down and when it is pushed down
and released, it accelerates up. It means a floating body experiences a net force towards its stable equilibrium position. Hence, a floating body oscillates when displaced up or down from its mean position.

 Consider a solid cylinder of density \sigma and height h, is floating in a liquid of density \rho as shown below figure,  And  \left( \sigma < \rho \right) .

 

If l is the length of cylinder dipping in liquid as shown in the above figure.

 

\\ \ at \ \ mean \ position \\ \ \ \ F_{net}=0\Rightarrow Weight \ of \ \ solid=buoyant \ \ force\Rightarrow mg=V\rho g\\ As \ m=\sigma hA\\ \Rightarrow \sigma hAg=\rho lAg \\ \Rightarrow l= \frac{h\sigma }{\rho }

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Riya

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