NEET · Physics · STD 11 - 9.2 surface tension

The amount of energy required to form a soap bubble of radius \(2\,cm\) from a soap solution is nearly \(..........\,\times 10^{-4}\,J\): (surface tension of soap solution \(=0.03\,N\,m ^{-1}\) )

A \(50.1\)
B \(30.16\)
C \(5.06\)
D \(3.01\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(3.01\)

Step-by-step Solution

Detailed explanation

\(E =2 T \left(4 \pi R ^3\right)\) \(=2(0.03)(4)(3.14)\left(2 \times 10^{-2}\right)^2\)

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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Match List \(I\) with List \(II\).

List I (Complex)	List \(II\) (Type of isomerism)
\(A\). \(\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_5\left(\mathrm{NO}_2\right)\right] \mathrm{Cl}_2\)	\(I\). Solvate isomerism
\(B\). \(\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_5\left(\mathrm{SO}_4\right)\right] \mathrm{Br}\)	\(II\). Linkage isomerism
\(C\). \(\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_6\right]\left[\mathrm{Cr}(\mathrm{CN})_6\right]\)	\(III\). Ionization isomerism
\(D\). \(\left[\mathrm{Co}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right] \mathrm{Cl}_3\)	\(IV\). Coordination isomerism

Choose the correct answer from the options given below:

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