JEE Mains · Physics · STD 11 - 9.1 fluid mechanics
A sphere of relative density \(\sigma\) and diameter \(D\) has concentric cavity of diameter \(d\). The ratio of \(\frac{D}{d}\), if it just floats on water in a tank is _______.
- A \(\left(\frac{\sigma}{\sigma-1}\right)^{\frac{1}{3}}\)
- B \(\left(\frac{\sigma+1}{\sigma-1}\right)^{\frac{1}{3}}\)
- C \(\left(\frac{\sigma-1}{\sigma}\right)^{\frac{1}{3}}\)
- D \(\left(\frac{\sigma-2}{\sigma+2}\right)^{\frac{1}{3}}\)
Answer & Solution
Correct Answer
(A) \(\left(\frac{\sigma}{\sigma-1}\right)^{\frac{1}{3}}\)
Step-by-step Solution
Detailed explanation
\(\text { weight (w) }=\frac{4}{3} \pi\left(\frac{D^3-d^3}{8}\right) \sigma g\) Buoyant force \(\left(F_b\right)=1 \times \frac{4}{3} \pi\left(\frac{D^3}{8}\right) \cdot g\) For Just Float \(\Rightarrow \mathrm{W}=\mathrm{F}_{\mathrm{b}}\)…
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