Two steel marbles (of radii R andR/3) are released in a highly viscous

1.	Two steel marbles (of radii R andR/3) are released in a highly viscous liquid. The ratio of the terminal velocity of the larger marble to that of the smaller is(A) 9 (B) 3 (C) 1 (D) R 1/9
Answer» Correct Option is (A) = 9 Given, \(r_1 = R\) \(r_2 = \frac{R}{3}\) The terminal velocity \(v = \frac{2}{9} \frac{r^2 (\rho - \sigma)g}{\eta}\) where, r = radius of falling body \(\eta\) = cofficient of viscosity g = gravity constant \(\rho\) = density of the falling body \(\sigma\) = density of fluid \(v_1 \propto r^2\) \(\frac{v_1}{v_2} = \frac{r_1{^2}}{r_2{^2}}\) \(\frac{v_1}{v_2} \frac{R^2}{\left(\frac{R}{3}\right)^2}\) \(\frac{v_1}{v_2} = \frac{9R^2}{R^2}\) \(\frac{v_1}{v_2} = \frac{9}{1}\) \(\Rightarrow 9\) Correct option is (A) 9

Two steel marbles (of radii R andR/3) are released in a highly viscous liquid. The ratio of the terminal velocity of the larger marble to that of the smaller is(A) 9 (B) 3 (C) 1 (D) R 1/9

Answer»

Correct Option is (A) = 9

Given,

\(r_1 = R\)

\(r_2 = \frac{R}{3}\)

The terminal velocity \(v = \frac{2}{9} \frac{r^2 (\rho - \sigma)g}{\eta}\)

where,

r = radius of falling body

\(\eta\) = cofficient of viscosity

g = gravity constant

\(\rho\) = density of the falling body

\(\sigma\) = density of fluid

\(v_1 \propto r^2\)

\(\frac{v_1}{v_2} = \frac{r_1{^2}}{r_2{^2}}\)

\(\frac{v_1}{v_2} \frac{R^2}{\left(\frac{R}{3}\right)^2}\)

\(\frac{v_1}{v_2} = \frac{9R^2}{R^2}\)

\(\frac{v_1}{v_2} = \frac{9}{1}\) \(\Rightarrow 9\)

Correct option is (A) 9