# A vertical cylinderical tank 1cm high has its top end closed by a tightly fitted frictionless piston of negligible weight.The air inside the cylinder is at an absolute pressure of 1atm.The piston is depressed by pouring mercury on it very slowly.How far will the piston before mercury spills on the top of cylinder?

$\begin{array}{1 1}(A)\;12cm\\(B)\;18cm\\(C)\;24cm\\(D)\;30cm\end{array}$

$\large\frac{xA\times \rho_{mercury}}{A}=\frac{x\times \rho_0\times A}{(100-x)A}$
$100\rho-\rho x=\rho_0$
$x=24cm$
Hence (C) is the correct answer.