Mercury is filled in a tube of radius 2 cm up to a height of 30 cm. The force exerted by mercury on the bottom of the tube is ________ N.

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Solution

Q.
Mercury is filled in a tube of radius 2 cm up to a height of 30 cm. The force exerted by mercury on the bottom of the tube is ________ N.

$(G i v e n, a t m o s p h e r i c p r e s s u r e = 10^{5}$ $N m^{- 2}, d e n s i t y o f m e r c u r y 1.36 \times 10^{4} k g$ $m^{- 3}, g = 10$ $m s^{- 2}, π = \frac{22}{7})$ [2024]

Ans.
(177) $P = P_{0} + ρ g h$

$F = P_{0} A + ρ g h A = \frac{22}{7} \times 4 \times 10^{- 4} (10^{5} + 1.36 \times 10^{4} \times 10 \times \frac{30}{100})$

$\Rightarrow F = \frac{88}{7} \times 10^{- 4} (10^{5} + 0.408 \times 10^{5})$

$= \frac{88}{7} \times 10 \times 1.408 = 177$

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