Question 206: Properties of Matter

Question

A uniform cylinder of length $L$ and mass $M$ having cross-sectional area $A$ is suspended, with its length vertical, from a fixed point by a mass-less spring such that it is half submerged in a liquid of density $\sigma $ at equilibrium position. The extension ${x_0}$ of the spring when it is in equilibrium is:

Accepted Answer

From figure, $k{x_0} + {F_B} = Mg$
$k{x_0} + \sigma {L \over 2}Ag = Mg$
[ as mass $=$ density  $ 	imes $ volume ]
$ \Rightarrow k{x_0} = Mg - \sigma {L \over 2}Ag$
$ \Rightarrow {x_0} = {{Mg - {{\sigma LAg} \over 2}} \over k}$
$ = {{Mg} \over k}\left( {1 - {{LA\sigma } \over {2M}}} ight)$

Answer

${{Mg} \over k}$

Answer

${{Mg} \over k}\left( {1 - {{LA\sigma } \over M}} \right)$

Answer

${{Mg} \over k}\left( {1 - {{LA\sigma } \over {2M}}} \right)$

Answer

${{Mg} \over k}\left( {1 + {{LA\sigma } \over M}} \right)$

Properties of Matter

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