Mercury is filled in a tube of radius $2 \mathrm{~cm}$ up to a height of $30 \mathrm{~cm}$. The force exerted by mercury on the bottom of the tube is. . . . . . $\mathrm{N}$.
(Given, atmospheric pressure $=10^5 \mathrm{Nm}^{-2}$, density of mercury $=1.36 \times 10^4 \mathrm{~kg} \mathrm{~m}^3, \mathrm{~g}=10 \mathrm{~ms}^2$, $\left.\pi=\frac{22}{7}\right)$
JEE MAIN 2024, Diffcult
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$\mathrm{F}=\mathrm{P}_0 \mathrm{~A}+\rho_{\mathrm{m}} \mathrm{ghA}$
$=10^5 \times \frac{22}{7} \times\left(2 \times 10^{-2}\right)^2$
$+1.36 \times 10^4 \times 10 \times\left(30 \times 10^{-2}\right)\left(\frac{22}{7} \times\left(2 \times 10^{-2}\right)^2\right)$
$\mathrm{F}=51.29+125.71=177 \mathrm{~N}$
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