JEE Main 2020PhysicsMechanical Properties of FluidsHardMCQ

JEE Main 2020 — Mechanical Properties of Fluids Question with Solution

JEE Main 2020 (08 Jan Shift 1)

Question

Consider a solid sphere of radius R and mass density ρr=ρ01-r2R2,0<r≤R. The minimum density of a liquid in which it will float is:

Choose an option

Show full solutionCorrect option: C
Correct answer
C2ρ05

Step-by-step explanation

The density of any point inside the sphere is

ρ=ρ01-r2R2   0<r≤R

weight = buoyant force
mg = B

mg=ρLVg
∫ρ4πr2drg=ρL43πR3g
∫0Rρ01-r2R24πr2dr=ρL43πR3
∫0Rρ04πr2-r4R2dr=ρ04πr33-r55R20R=ρL43πR3
25ρ0=ρL

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About this question

This is a previous-year question from JEE Main 2020, covering the Mechanical Properties of Fluids chapter of Physics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.