Question

The bulk modulus of a spherical object is 'B'. If it is subjected to uniform pressure 'p', the fractional decrease in radius is :-

Answer 1

Answer is option (3) p/3B.

\({\text{volume of sphere}},V = \frac{4}{3}\pi r^3\)

Differentiate both sides with respect to r

\(\frac{dV}{dr}=4\pi r^2\\\\\Delta{V}=4\pi r^2\Delta{r}\\\\\text{dividing by},V=\frac{4}{3}\pi r^3\\\\\frac{\Delta V}{V} =3\frac{\Delta r}{r}\)

Bulk modulus is given by

Comments

Please explain.... Why 3 is multiplied over here

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Because, this is rule in combination of errors