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A uniform solid cylinder of density 0.8 g / cm3 floats in equilibrium in a combination of two non-mixing liquids A and B with its axis vertical. The densities of the liquids A and B with its axis vertical. The densities of the liquids A and B are 0.7 g/cm3 and 1.2 g/cm3, respectively. The height of liquid A is hA = 1.2 cm. The length of the part of the cylinder immersed in liquid B is hB = 0.8 cm.
  1. Find the total force exerted by liquid A on the cylinder.
  2. Find h, the length of the park of the cylinder in air.
  3. The cylinder is depressed in such a way that its top surface is just below the upper surface of liquid A and is then released. Find the acceleration of the cylinder immediately after it is released.

Radhika Batra , 10 Years ago
Grade 11
anser 1 Answers
Kevin Nash

Last Activity: 10 Years ago

Hello Student,
Please find the answer to your question
. (a) As the pressure exerted by liquid A on the cylinder is radial and symmetric, the force due to this pressure cancels out and the net value is zero .
(b) For equilibrium, Buoyant force = weight of the body
⇒ hA pA Ag + hB ρB Ag = (hA + h + hB) A ρCg
(where pC = density of cylinder )
h = (hA pA + hB pB / pc) – (hA + hB) = 0.25 cm
(c) a = FBuoyant – Mg / M
= [hA ρA + ρB (h + hB) – (h + hA + hB) ρc / ρC (h + hA +hC)]g
= g / 6 upwards
Thanks
Kevin Nash
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