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KVPY Sample Paper KVPY Stream-SX Model Paper-31

  • question_answer
    What is the radius of a steel sphere that will float on water with exactly half the sphere submerged? Density of steel is \[7.9\times {{10}^{3}}kg/{{m}^{3}}\]and surface tension of water is \[7\times {{10}^{-2}}N\]

    A) \[2.6\,cm\]

    B) \[4.6\,mm\]

    C) \[1.2\,mm\]

    D) \[6.5\,mm\]

    Correct Answer: C

    Solution :

    Surface tension force + upthrust = weight
    \[(2\pi rT)+\left( \frac{2}{3}\pi {{r}^{3}} \right){{p}_{W}}g=\left( \frac{4}{3}\pi r3 \right){{p}_{S}}g\]
    Substituting the values, we get
    \[r\approx 1.2mm\]


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