A Spherical ball of radius 1mm and density 10.5 g/cc is dropped in… | JEE Main 2023 (24 Jan, Shift 2)

Q17JEE Main 2023 · 24 JAN · SHIFT 2Medium

Viscosity & Stokes' Law

A Spherical ball of radius 1mm and density 10.5 g/cc is dropped in glycerine of coefficient of viscosity 9.8 poise and density 1.5 g/cc. Viscous force on the ball when it attains constant velocity is $3696 \times 10^{-x}$ N. The value of $x$ is ________.

(Given, g = 9.8 m/s $^{2}$ and $\pi = \frac{22}{7}$ )

Numerical answer type. Work it out, then open the answer.

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Answer: 7

At constant velocity: $F_v = W - B = \frac{4}{3}\pi r^3(\rho - \sigma)g$ .
$r = 10^{-3}$ m, $\rho - \sigma = 9\text{ g/cc} = 9000\text{ kg/m}^3$ .
$F_v = \frac{4}{3}\cdot\frac{22}{7}\cdot10^{-9}\cdot9000\cdot9.8 = 3696\times10^{-7}$ N
So $x = 7$ .

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