A solid sphere of radius R made of a material | vedclass

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(B) The volume of the sphere is $V = \frac{4}{3} \pi R^3$. Taking the logarithmic derivative,we get $\frac{\delta V}{V} = 3 \frac{\delta R}{R}$. The p

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$mg/3AK$

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(B) The volume of the sphere is $V = \frac{4}{3} \pi R^3$. Taking the logarithmic derivative,we get $\frac{\delta V}{V} = 3 \frac{\delta R}{R}$. The pressure exerted on the liquid by the piston is $P = \frac{mg}{A}$. By the definition of bulk modulus,$K = -\frac{P}{\delta V / V}$. Substituting the expressions for $P$ and $\frac{\delta V}{V}$,we have $K = -\frac{mg/A}{3 \delta R / R}$. Rearranging for the fractional change in radius,we get $\frac{\delta R}{R} = -\frac{mg}{3AK}$. The negative sign indicates a decrease in radius due to compression.

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