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Properties of Matter question

2008 · Shift 1 · Q63
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Properties of Matter question

2008 · Shift 1 · Q63

JEE AdvancedPhysicsProperties of MatterMCQ+3 / −1
A small spherical monoatomic ideal gas bubble (γ=53)\left( {\gamma = {5 \over 3}} \right)(γ=35​) is trapped inside a liquid of density ρ1\rho_1ρ1​ (see figure). Assume that the bubble does not exchange any heat with the liquid. The bubble contains n moles of gas. The temperature of the gas when the bubble is at the bottom is T 0_00​, the height of the liquid is H and the atmospheric pressure is P 0_00​ (Neglect surface tension) IIT-JEE 2008 Paper 1 Offline Physics - Properties of Matter Question 10 English ComprehensionThe buoyancy force acting on the gas bubble is (Assume R is the universal gas constant)
  1. A
    ρlnRgT0(P0+ρlgH)25(P0+ρlgy)75{\rho _l}nRg{T_0}{{{{({P_0} + {\rho _l}gH)}^{{2 \over 5}}}} \over {{{({P_0} + {\rho _l}gy)}^{{7 \over 5}}}}}ρl​nRgT0​(P0​+ρl​gy)57​(P0​+ρl​gH)52​​
  2. B
    ρlnRgT0(P0+ρlgH)25[P0+ρlg(H−y)]35{{{\rho _l}nRg{T_0}} \over {{{({P_0} + {\rho _l}gH)}^{{2 \over 5}}}{{[{P_0} + {\rho _l}g(H - y)]}^{{3 \over 5}}}}}(P0​+ρl​gH)52​[P0​+ρl​g(H−y)]53​ρl​nRgT0​​
  3. C
    ρlnRgT0(P0+ρlgH)35(P0+ρlgy)85{\rho _l}nRg{T_0}{{{{({P_0} + {\rho _l}gH)}^{{3 \over 5}}}} \over {{{({P_0} + {\rho _l}gy)}^{{8 \over 5}}}}}ρl​nRgT0​(P0​+ρl​gy)58​(P0​+ρl​gH)53​​
  4. D
    ρlnRgT0(P0+ρlgH)35[P0+ρlg(H−y)25{{{\rho _l}nRg{T_0}} \over {{{({P_0} + {\rho _l}gH)}^{{3 \over 5}}}[{P_0} + {\rho _l}g{{(H - y)}^{{2 \over 5}}}}}(P0​+ρl​gH)53​[P0​+ρl​g(H−y)52​ρl​nRgT0​​
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