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JEE Advanced 2011Paper 2
Exam
JEE Advanced
Year
2011
Paper
Paper 2
Subject
Physics
Chapter
Mechanical Properties of Fluids

JEE Advanced 2011 · Paper 2 · Physics · Mechanical Properties of Fluids

Two solid spheres A and B of equal volumes but of different...

Two solid spheres AA and BB of equal volumes but of different densities dAd_A and dBd_B are connected by a string. They are fully immersed in a fluid of density dFd_F. They get arranged into an equilibrium state as shown in the figure with a tension in the string. The arrangement is possible only if Two solid spheres A and B of equal volumes but of different densities d_A and d_B are connected by a string. They are

Options

  1. AdA<dFd_A < d_F
  2. BdB>dFd_B>d_F
  3. CdA>dFd_A>d_F
  4. DdA+dB=2dFd_A+d_B=2 d_F

Correct answer

A. dA<dFd_A < d_F

Step-by-step solution

Two solid spheres A and B of equal volumes but of different densities d_A and d_B are connected by a string. They are
Equilibrium of AAVdFg=T+WA=T+VdAg\begin{aligned}V d_F g & =T+W_A \\ & =T+V d_A g \end{aligned}EquilibriumEquilibrium of B,T+VdFg=VdBgAddingEqs.(i)and(ii),weget, T+V d_F g=V d_B g Adding Eqs. (i) and (ii), we get2 d_f=d_A+d_B\thereforeOption (d) is correct. From Eq.(i),wecanseethatdF>dAEq. (i), we can see that d_F>d_A \quad\text{ [as }T>0T>0\text{ ] }\thereforeOption(a)iscorrect.FromEq.(ii)wecanseethat,dB>dFOption (a) is correct. From Eq. (ii) we can see that, d_B>d_F\thereforeOption(a)iscorrect.Option (a) is correct.\therefore Correct options are (a), (b) and (d). Analysis of Question Question is moderately difficult but conceptwise it is good.
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