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

Correct answer: (D) 0.1 ~m / s. fracv_sv_g=frac (ρ_s-ρ_ℓ ) (ρ_g-ρ_ℓ ) v_s=0.1 ~m / s

Q133 / 150 · JEE Main 2006 · Physics

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

A
$0.2 \mathrm{~m} / \mathrm{s}$
B
$0.4 \mathrm{~m} / \mathrm{s}$
C
$0.133 \mathrm{~m} / \mathrm{s}$
Correct answer
D
$0.1 \mathrm{~m} / \mathrm{s}$

Solution

$\frac{\mathrm{v}_{\mathrm{s}}}{\mathrm{v}_{\mathrm{g}}}=\frac{\left(\rho_{\mathrm{s}}-\rho_{\ell}\right)}{\left(\rho_{\mathrm{g}}-\rho_{\ell}\right)}$ $\mathrm{v}_{\mathrm{s}}=0.1 \mathrm{~m} / \mathrm{s}$

Hence, the correct answer is option: 'D'.

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