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Grade 11Mechanics

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 h_A = 1.2 cm. The length of the part of the cylinder immersed in liquid B is h_B = 0.8 cm.

Find the total force exerted by liquid A on the cylinder.

Find h, the length of the park of the cylinder in air.

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.

Question image for A uniform solid cylinder of density 0.8 g / cm 3 f

Radhika Batra

12 Years agoGrade 11

1 Answer

Kevin Nash

12 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

⇒ h_A p_A Ag + h_B ρ_B Ag = (h_A + h + h_B) A ρ_Cg

(where p_C = density of cylinder )

h = (h_A p_{A +}h_B p_B/ pc) – (h_{A +}h_B) = 0.25 cm

(c) a = F_Buoyant – Mg / M

= [h_A ρ_A + ρ_B (h + h_B) – (h + h_A + h_B) ρ_c / ρ_C (h + h_A +h_C)]g

= g / 6 upwards

Thanks
Kevin Nash
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