Fluid MechanicsHard

Question

A 10 cm side cube weighing 5N is immersed in a liquid of relative density 0.8 contained in a rectangular tank of cross section a area 15cm x 15cm. If the tank contained liquid to a height of 8 cm before the immersion, the level of the liquid surface is :

Options

A. cm
B. cm
C.10 cm
D.11 cm

Solution

Given: ρc × (10)3 × g = 5 × 105 dynes ⇒ ρc = 0.5; g = 1000 cm/s2, Buoyant force should balance weight ⇒ ρl Vl g = 5 × 105 ⇒ Vl = 625 cm3, ∴ depth upto which cube is dipped is ⇒ 625 = 10 × 10 × d   ⇒ d = 6.25 cm. Now, 15 × 15 × h = 15 × 15 × 8 + 625   ⇒   h = 97/9 [ ρc (density of cube), ρl (density of liquid), Vl (volume of liquid displacement)]

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