Mercury is completely filled in a rectangular tank of height 72 cm. The atmospheric pressure at the place is 72 cm of Hg. Find the distance in cm of point of application from bottom of tank of the net force, on the inner surface of the side vertical wall of tank.

Question

Mercury is completely filled in a rectangular tank of height 72 cm. The atmospheric pressure at the place is 72 cm of Hg. Find the distance in cm of point of application from bottom of tank of the net force, on the inner surface of the side vertical wall of tank., 32 cm, 16 cm, 74 cm, 42 cm

MARKS App · Accepted Answer

Force due to atmospheric pressure = ρ 0 A = ρ​gH × bH F 1 = ​ρgbH 2 ​ Force due to mercury on side wall, F 2 = ρ g b H 2 2 This force acts at a height H 1 = H/2 from bottom This force acts at a height H 2 = H/3 from bottom. ∴ distance of net force from bottom = F 1 H 2 + F 2 H 2 F 1 + F 2 = ρ g b H 2 × H 2 + ρ gb × H 2 2 × H 3 ρ gb H 2 + ρ gb H 2 2 = 4 9 H = 32 cm.

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