Fluid Mechanics

JEE Main level, single correct, medium

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Question 191 of 192

If the terminal speed of a sphere of gold (density =19.5 kg/m3=19.5 \mathrm{~kg} / \mathrm{m}^3 ) is 0.2 m/s0.2 \mathrm{~m} / \mathrm{s} in a viscous liquid (density =1.5 kg/m3=1.5 \mathrm{~kg} / \mathrm{m}^3 ) of the same size in the same liquid.

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Answer: (D) 0.1 m/s0.1 \mathrm{~m} / \mathrm{s}

vsvg=(ρs−ρℓ)(ρg−ρℓ)\frac{\mathrm{v}_{\mathrm{s}}}{\mathrm{v}_{\mathrm{g}}}=\frac{\left(\rho_{\mathrm{s}}-\rho_{\ell}\right)}{\left(\rho_{\mathrm{g}}-\rho_{\ell}\right)}
vs=0.1 m/s\mathrm{v}_{\mathrm{s}}=0.1 \mathrm{~m} / \mathrm{s}

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