MHT CET · Physics · Mechanical Properties of Solids

A rubber ball be taken in a deep sea so that its volume is decreased by \(x \%\). The
bulk modulus of rubber is 'K' and density of sea water is ' \(\varrho\) '. The depth to whÃch a rubber ball is taken is proportional to \((\mathrm{g}=\) acceleration due to gravity)

A \(\frac{\text { ex }}{\mathrm{Kg}}\)
B \(\frac{\mathrm{Kx}}{\mathrm{eg}}\)
C \(\frac{\mathrm{eg}}{\mathrm{Kx}}\)
D \(\frac{\mathrm{Q}}{\mathrm{Kxg}}\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{\mathrm{Kx}}{\mathrm{eg}}\)

Step-by-step Solution

Detailed explanation

\(B=-\frac{\Delta p}{\Delta v / v}\)
\(\frac{\Delta v}{v}=\frac{x}{100}...(1)\)
\(\Delta p=\rho g h\)
\(\frac{\rho g h}{x / 100}\)
\(h \propto \frac{k x}{\rho g}\)

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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A rubber ball be taken in a deep sea so that its volume is decreased by \(x \%\). Thebulk modulus of rubber is 'K' and density of sea water is ' \(\varrho\) '. The depth to whÃ­ch a rubber ball is taken is proportional to \((\mathrm{g}=\) acceleration due to gravity)

Step-by-step Solution

A rubber ball be taken in a deep sea so that its volume is decreased by \(x \%\). The
bulk modulus of rubber is 'K' and density of sea water is ' \(\varrho\) '. The depth to whÃch a rubber ball is taken is proportional to \((\mathrm{g}=\) acceleration due to gravity)