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  • A needle of length l and density  will float on a liquid of surface tension <img

A needle of length l and density \mathrm{ \rho} will float on a liquid of surface tension \mathrm{ \sigma} if its radius r is less than or equal to

Option: 1

\mathrm{\sqrt{\frac{2 \sigma}{\pi \rho \lg }}}


Option: 2

\mathrm{\sqrt{\frac{2 \sigma l}{\pi \rho g}}}


Option: 3

\mathrm{\sqrt{\frac{\sigma}{\pi \rho g}}}


Option: 4

\mathrm{\sqrt{\frac{2 \sigma}{\pi \rho g}}}


Answers (1)

best_answer

Force per unit area exerted on the needle due to liquid is

                                    \mathrm{ P_1=\frac{\sigma}{r} }
Pressure exerted by needle on the liquid is

\mathrm{ P_2=\frac{m g}{l(2 r)}=\frac{\pi r^2 l \rho g}{2 l r}=\frac{\pi r \rho g}{2} }

For equilibrium, \mathrm{P_1=P_2}, i.e.

or         \mathrm{ \begin{aligned} \frac{\sigma}{r} & =\frac{\pi r \rho g}{2} \\\\ r & =\sqrt{\frac{2 \sigma}{\pi \rho g}} \end{aligned} }

Posted by

jitender.kumar

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