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AP EAMCET · PHYSICS · Mechanical Properties of Fluids

A spherical body of density \(\rho\) is floating half immersed in a liquid of density \(d\). If \(\sigma\) is the surface tension of the liquid, then the diameter of the body is

  1. A \(\sqrt{\frac{3 \sigma}{g(2 \rho-d)}}\)
  2. B \(\sqrt{\frac{6 \sigma}{g(2 \rho-d)}}\)
  3. C \(\sqrt{\frac{4 \sigma}{g(2 \rho-d)}}\)
  4. D \(\sqrt{\frac{12 \sigma}{g(2 \rho-d)}}\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\sqrt{\frac{3 \sigma}{g(2 \rho-d)}}\)

Step-by-step Solution

Detailed explanation

Weight of body \(=\) Buoyant force + Force of surface tension \( \begin{aligned} \frac{4}{3} \pi r^3 \rho \times g & =\frac{2}{3} \pi r^3 d g+2 \pi r \sigma \\ \frac{2}{3} \pi r^3 g(2 \rho-d) & =2 \pi r \sigma \end{aligned} \) So, \(r^2=\frac{3 \sigma}{g(2 \rho-d)}\) So,…