Small water droplets of radius 0.01 ~mm are formed in the upper atmosphere and falling with a terminal velocity of 10 ~cm / s . Due to condensation, if 8 such droplets are coalesced and formed a larger drop, the new terminal velocity will be _____ cm / s .

Correct answer: 40. m= mass of small drop M= mass of bigger drop V_t=2/9 (R^2(ρ-σ) g)/(η) 8 ∝ m=M 8 r^3=R^3 ⇒ R=2 R as V_t × R^2 ∵ Radius double so V_t becomes 4 time ∴ 4 × 10=40 ~cm / s

Q86 / 90 · JEE Main 2024 (08 Apr Shift 2) · Physics

Small water droplets of radius $0.01 \mathrm{~mm}$ are formed in the upper atmosphere and falling with a terminal velocity of $10 \mathrm{~cm} / \mathrm{s}$. Due to condensation, if 8 such droplets are coalesced and formed a larger drop, the new terminal velocity will be _____$\mathrm{cm} / \mathrm{s}$.

Correct answer: 40

Solution

$\mathrm{m}=$ mass of small drop $\mathrm{M}=$ mass of bigger drop $\begin{aligned} & V_t=\frac{2}{9} \frac{R^2(\rho-\sigma) g}{\eta} \\ & 8 \propto m=M \\ & 8 r^3=R^3 \Rightarrow R=2 R\end{aligned}$ as $\mathrm{V}_{\mathrm{t}} \times \mathrm{R}^2 \quad \because$ Radius double so $\mathrm{V}_{\mathrm{t}}$ becomes 4 time $\therefore 4 \times 10=40 \mathrm{~cm} / \mathrm{s}$

Hence, the correct answer is 40.

Relevant Questions

A spherical liquid drop of radius acquires the terminal velocity when falls through a gas of viscosity . Now the drop is broken into identic08 Apr, 2026 (E)Viscosity
If an air bubble of diameter mm rises steadily through a liquid of density kg/m at a rate of cm/s, then the coefficient of viscosity of liqu02 Apr, 2026 (E)Viscosity
Sixty four rain drops of radius 1 mm each falling down with a terminal velocity of coalesce to form a bigger drop. The terminal velocity of 24 Jan, 2026 (M)Viscosity
A small metallic sphere of diameter 2 mm and density is dropped in glycerine having viscosity 10 Poise and density respectively. The termina23 Jan, 2026 (E)Viscosity
A spherical body of radius and density falls freely through a viscous liquid having density and viscosity and attains a terminal velocity . 21 Jan, 2026 (E)Viscosity
The terminal velocity of a metallic ball of radius 6 mm in a viscous fluid is . The terminal velocity of another ball of same material and h21 Jan, 2026 (E)Viscosity