JEE Main & Advanced Physics Fluid Mechanics, Surface Tension & Viscosity / द्रव यांत्रिकी, भूतल तनाव और चिपचिपापन Question Bank Self Evaluation Test - Mechanical Properties of Fluids

  • question_answer
    A certain number of spherical drops of a liquid of radius 'r' coalesce to form a single drop of radius 'R' and volume 'V'. If 'T' is the surface tension of the liquid, then:

    A) \[energy=4VT\text{ }\left( \frac{1}{r}-\frac{1}{R} \right)\text{ }is\text{ }released\]

    B) \[energy\text{ }=3VT\text{ }\left( \frac{1}{r}+\frac{1}{R} \right)is\text{ }absorbed\]

    C) \[energy\text{ }=\text{ }3VT\left( \frac{1}{r}-\frac{1}{R} \right)is\text{ }released\]

    D) Energy is neither released nor absorbed

    Correct Answer: C

    Solution :

    [c] As surface area decreases so energy is released. Energy released\[=4\pi {{R}^{2}}T[{{n}^{1/3}}-1]\] (where\[R={{n}^{1/3}}r\]) \[=4\pi {{R}^{3}}T\left[ \frac{1}{r}-\frac{1}{R} \right]=3VT\left[ \frac{1}{r}-\frac{1}{R} \right]\]


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