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AP EAMCET · PHYSICS · Mechanical Properties of Fluids

A sphere of material of relative density 8 has a concentric spherical cavity and just sinks in water. If the radius of the sphere is \(2 \mathrm{~cm}\), then the volume of the cavity is

  1. A \(\frac{76}{3} \mathrm{~cm}^3\)
  2. B \(\frac{79}{3} \mathrm{~cm}^3\)
  3. C \(\frac{82}{3} \mathrm{~cm}^3\)
  4. D \(\frac{88}{3} \mathrm{~cm}^3\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{88}{3} \mathrm{~cm}^3\)

Step-by-step Solution

Detailed explanation

Let \(r\) be the radius of cavity \(\therefore\) Volume of cavity \(=\frac{4}{3} \pi \mathrm{r}^3\) Now, \(\frac{4}{3} \pi\left(R^3-r^3\right) d m g=\frac{4}{3} \pi R^3 d_w g\) \(\Rightarrow 1-\frac{R^3}{r^3}=\frac{1}{8} \Rightarrow \frac{R^3}{r^3}=1-\frac{1}{8}\)…