MHT CET · Physics · Mechanical Properties of Fluids

In air, a charged soap bubble of radius ‘ $R$ ’ breaks into $27$ small soap bubbles of equal radius ‘ $r$ ’. Then, the ratio of mechanical force acting per unit area of big soap bubble to that of a small soap bubble is

A $\frac{1}{81}$
B $\frac{3}{1}$
C $\frac{1}{3}$
D $\frac{9}{1}$

Verified Solution

Answer & Solution

Correct Answer

(D) $\frac{9}{1}$

Step-by-step Solution

Detailed explanation

∵ R = (n^{\frac{1}{3}}) . r

R = {(27)}^{\frac{1}{3}} . r

R = 3 r

∴ \frac{F}{A} \propto \frac{1}{r^{2}}

\frac{(\frac{F}{A}) B i g}{(\frac{F}{A}) S m a l l} = \frac{1}{\frac{{(3 r)}^{2}}{\frac{1}{r^{2}}}} = \frac{1}{9}

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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In air, a charged soap bubble of radius ‘ R ’ breaks into 27 small soap bubbles of equal radius ‘ r ’. Then, the ratio of mechanical force acting per unit area of big soap bubble to that of a small soap bubble is

Step-by-step Solution

In air, a charged soap bubble of radius ‘ $R$ ’ breaks into $27$ small soap bubbles of equal radius ‘ $r$ ’. Then, the ratio of mechanical force acting per unit area of big soap bubble to that of a small soap bubble is