Q89 / 90 · JEE Main 2024 (04 Apr Shift 2) · Physics
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 _____ N.
(Given, atmospheric pressure $=10^5 \mathrm{Nm}^{-2}$, density of mercury $=1.36 \times 10^4 \mathrm{~kg} \mathrm{~m}^{-}$ $\left.{ }^3, \mathrm{~g}=10 \mathrm{~m} \mathrm{~s}^{-2}, \pi=\frac{22}{7}\right)$
Correct answer: 177
Solution
$\begin{aligned} & \mathrm{F}=\mathrm{P}_0 \mathrm{~A}+\rho_{\mathrm{m}} \mathrm{ghA} \\ & =10^5 \times \frac{22}{7} \times\left(2 \times 10^{-2}\right)^2 \\ & +1.36 \times 10^4 \times 10 \times\left(30 \times 10^{-2}\right)\left(\frac{22}{7} \times\left(2 \times 10^{-2}\right)^2\right) \\ & \mathrm{F}=51.29+125.71=177 \mathrm{~N}\end{aligned}$
Hence, the correct answer is 177.