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MHT CET · Physics · Mechanical Properties of Fluids

A metal sphere of radius 'R', density ' \(\varrho_{1}\) ' moves with terminal velocity ' \(\mathrm{v}_{1}\) ' through
a liquid of density ' \(\sigma^{\prime}\). Another sphere of same radius but of density ' \(\varrho_{2}\) ' moves
through same liquid. Its terminal velocity will be

  1. A \(\left[\frac{\varrho_{1}-\varrho_{2}}{\sigma}\right] \mathrm{v}_{1}\)
  2. B \(\left[\frac{\varrho_{2}+\sigma}{\varrho_{1}+\sigma}\right] \mathrm{v}_{1}\)
  3. C \(\left[\frac{\varrho_{1}+\varrho_{2}}{\sigma}\right] \mathrm{v}_{1}\)
  4. D \(\left[\frac{\mathrm{e}_{2}-\sigma}{\mathrm{e}_{1}-\sigma}\right] \mathrm{v}_{1}\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\left[\frac{\mathrm{e}_{2}-\sigma}{\mathrm{e}_{1}-\sigma}\right] \mathrm{v}_{1}\)

Step-by-step Solution

Detailed explanation

\(6 \pi \eta R v_{1}=\frac{4}{3} \pi R^{3}(\rho_{1}-\sigma)\)
\(6 \pi \eta R v_{2}=\frac{4}{3} \pi R^{3}\left(\rho_{2}-\sigma\right)\)
\(\therefore \frac{v_{2}}{v_{1}}=\frac{\rho_{2}-\sigma}{\rho_{1}-\sigma}\)
\(v_{2}=\frac{\rho_{2}-\sigma}{\rho_{1}-\sigma} v_{1}\)
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