The velocity of a small ball of mass 0.3 g and density 8 g/cc when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is 1.3 g/cc, then the value of viscous force acting on the ball will be x × 10⁻⁴ N. The value of x is _________. [use g = 10 m/s²] Numerical answer type. Work it out, then open the answer.

Answer: 25. At constant velocity: Fv = mg(1 - (σ)/(ρ)). Fv = (0.3×10⁻³)(10)(1 - 1.3/8) = 3×10⁻³×0.8375 Fv ≈ 2.51×10⁻³ = 25×10⁻⁴ N So x ≈ 25.

The velocity of a small ball of mass 0.3 g and density 8 g/cc when… | JEE Main 2022 (29 Jul, Shift 2)

Q22JEE Main 2022 · 29 JUL · SHIFT 2Medium

Viscosity & Stokes' Law

The velocity of a small ball of mass $0.3\text{ g}$ and density $8\text{ g/cc}$ when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is $1.3\text{ g/cc}$ , then the value of viscous force acting on the ball will be $x \times 10^{-4}\text{ N}$ . The value of $x$ is _________. [use $\mathrm{g} = 10\text{ m/s}^{2}]$

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

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Answer: 25

At constant velocity: $F_v = mg\left(1 - \frac{\sigma}{\rho}\right)$ .
$F_v = (0.3\times10^{-3})(10)\left(1 - \frac{1.3}{8}\right) = 3\times10^{-3}\times0.8375$
$F_v \approx 2.51\times10^{-3} = 25\times10^{-4}$ N
So $x \approx 25$ .

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