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Properties of Matter question

2018 · 15 Apr · Shift 1 · Q63
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Properties of Matter question

2018 · 15 Apr · Shift 1 · Q63

JEE MainPhysicsProperties of MatterMCQ+4 / −1
A thin uniform tube is bent into a circle of radius rrr in the vertical plane. Equal volumes of two immiscible liquids, whose densities are ρ1{\rho _1}ρ1​ and ρ2{\rho _2}ρ2​ (ρ1>ρ2),\left( {{\rho _1} \gt {\rho _2}} \right),(ρ1​>ρ2​), fill half the circle. The angle θ\thetaθ between the radius vector passing through the common interface and the vertical is :
  1. A
    θ=tan⁡−1π(ρ1ρ2)\theta = {\tan ^{ - 1}}\pi \left( {{{{\rho _1}} \over {{\rho _2}}}} \right)θ=tan−1π(ρ2​ρ1​​)
  2. B
    θ=tan⁡−1π2(ρ1ρ2)\theta = {\tan ^{ - 1}}{\pi \over 2}\left( {{{{\rho _1}} \over {{\rho _2}}}} \right)θ=tan−12π​(ρ2​ρ1​​)
  3. C
    θ=tan⁡−1(ρ1−ρ2ρ1+ρ2)\theta = {\tan ^{ - 1}}\left( {{{{\rho _1} - {\rho _2}} \over {{\rho _1} + {\rho _2}}}} \right)θ=tan−1(ρ1​+ρ2​ρ1​−ρ2​​)
  4. D
    θ=tan⁡−1π2(ρ1+ρ2ρ1−ρ2)\theta = {\tan ^{ - 1}}{\pi \over 2}\left( {{{{\rho _1} + {\rho _2}} \over {{\rho _1} - {\rho _2}}}} \right)θ=tan−12π​(ρ1​−ρ2​ρ1​+ρ2​​)
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