MHT CET · Physics · Mechanical Properties of Fluids

Eight identical drops of water falling through air with uniform velocity of 10cm/s combine to form a single drop of big size, then terminal velocity of the big drop will be

A 80 cm/s
B 10 cm/s
C 30 cm/s
D 40 cm/s

Verified Solution

Answer & Solution

Correct Answer

(D) 40 cm/s

Step-by-step Solution

Detailed explanation

Given, terminal velocity of each small drop

v_{1} = \frac{10 c m}{s}

When 8 small drops are combined to form bigger
If

r_{1}

be radius of small drop and

r_{2}

be radius of bigger drop, then

v_{2} = v_{1}

\frac{4}{3} π r_{2}^{3} = 8 \times \frac{4}{3} π r_{1}^{3} \Rightarrow r_{2} = 2 r_{1}

∴

Terminal velocity of the drop

v = \frac{2 r^{2}}{9} \frac{(p - σ)}{9 η}

i.e.,

v \propto r^{2}

∴ \frac{v_{1}}{v_{2}} = \frac{r_{1}^{2}}{r_{2}^{2}} = \frac{r_{1}^{2}}{{(2 r_{1})}^{2}} \Rightarrow \frac{v_{1}}{v_{2}} = \frac{1}{4}

v_{2} = 4 v_{2} = 4 \times 10 = 40

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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