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Properties of Matter question

2008 · Shift 0 · Q76
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Properties of Matter question

2008 · Shift 0 · Q76

JEE MainPhysicsProperties of MatterMCQ+4 / −1
A jar is filled with two non-mixing liquids 111 and 222 having densities ρ1{\rho _1}ρ1​ and ρ2{\rho _2}ρ2​ respectively. A solid ball, made of a material of density ρ3{\rho _3}ρ3​, is dropped in the jar. It comes to equilibrium in the position shown in the figure. Which of the following is true for ρ1{\rho _1}ρ1​, ρ1{\rho _1}ρ1​ and ρ3{\rho _3}ρ3​ ? AIEEE 2008 Physics - Properties of Matter Question 262 English
  1. A
    ρ3<ρ1<ρ2{\rho _3} \lt {\rho _1} \lt \rho {}_2ρ3​<ρ1​<ρ2​
  2. B
    ρ1>ρ3>ρ2{\rho _1} \gt {\rho _3} \gt \rho {}_2ρ1​>ρ3​>ρ2​
  3. C
    ρ1<ρ2<ρ3{\rho _1} \lt {\rho _2} \lt \rho {}_3ρ1​<ρ2​<ρ3​
  4. D
    ρ1<ρ3<ρ2{\rho _1} \lt {\rho _3} \lt \rho {}_2ρ1​<ρ3​<ρ2​
View written solutionFree

Correct answer: D

  1. Understand the situation

    Two immiscible liquids settle in layers according to density:

    • the less dense liquid stays on top,
    • the more dense liquid stays below.

    So if liquid 111 is the upper layer and liquid 222 is the lower layer, then ρ1<ρ2.\rho_1 < \rho_2.ρ1​<ρ2​.

  2. Interpret the equilibrium position of the ball

    The ball is shown in equilibrium at the interface of the two liquids, which means:

    • it does not float completely on the top liquid, so its density must be greater than the top liquid density,
    • it does not sink completely into the bottom liquid, so its density must be less than the bottom liquid density.

    Therefore, ρ1<ρ3<ρ2.\rho_1 < \rho_3 < \rho_2.ρ1​<ρ3​<ρ2​.

  3. Check options

    • A: ρ3<ρ1<ρ2\rho_3 < \rho_1 < \rho_2ρ3​<ρ1​<ρ2​
      False, because then the ball would float entirely in the top liquid.

    • B: ρ1>ρ3>ρ2\rho_1 > \rho_3 > \rho_2ρ1​>ρ3​>ρ2​
      False, also contradicts the layering condition.

    • C: ρ1<ρ2<ρ3\rho_1 < \rho_2 < \rho_3ρ1​<ρ2​<ρ3​
      False, because then the ball would sink to the bottom.

    • D: ρ1<ρ3<ρ2\rho_1 < \rho_3 < \rho_2ρ1​<ρ3​<ρ2​
      True.

  4. Final answer

    ρ1<ρ3<ρ2\boxed{\rho_1 < \rho_3 < \rho_2}ρ1​<ρ3​<ρ2​​

    Hence, the correct option is D.

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