TS EAMCET · Physics · Mechanical Properties of Fluids
If the terminal velocity of a metal sphere of mass 8 g falling through a liquid is \(3 \mathrm{cms}^{-1}\), then the terminal velocity of another sphere of mass 64 g made of the same metal falling through same liquid is
- A \(6 \mathrm{cms}^{-1}\)
- B \(3 \mathrm{cms}^{-1}\)
- C \(12 \mathrm{cms}^{-1}\)
- D \(18 \mathrm{cms}^{-1}\)
Answer & Solution
Correct Answer
(C) \(12 \mathrm{cms}^{-1}\)
Step-by-step Solution
Detailed explanation
\(v_t \propto r^2\) \(m \propto r^3 \Rightarrow r \propto m^{1/3}\) \(v_t \propto (m^{1/3})^2 = m^{2/3}\) \(\frac{v_{t2}}{v_{t1}} = \left(\frac{m_2}{m_1}\right)^{2/3}\) \(\frac{v_{t2}}{3} = \left(\frac{64 \text{ g}}{8 \text{ g}}\right)^{2/3}\)…
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