A spherical ball of volume $2000 \mathrm{~cm}^3$ is subjected to a hydraulic pressure of $15 \mathrm{~atm}$.…

A spherical ball of volume $2000 \mathrm{~cm}^3$ is subjected to a hydraulic pressure of $15 \mathrm{~atm}$. If the change in volume is $5 \times 10^{-2} \mathrm{~cm}^3$, the bulk modules of the material of the spherical ball is $\left(1 \mathrm{~atm}=10^5 \mathrm{Nm}^{-2}\right)$
  1. $6 \times 10^{10} \mathrm{Nm}^{-2}$
  2. $2 \times 10^{10} \mathrm{Nm}^{-2}$
  3. $5 \times 10^{10} \mathrm{Nm}^{-2}$
  4. $15 \times 10^{10} \mathrm{Nm}^{-2}$

Solution

Volume of spherical ball, $V=2000 \times 10^{-6} \mathrm{~m}^3$ Hydraulic pressure, $\mathrm{P}=15 \mathrm{~atm}=15 \times 10^5 \mathrm{Nm}^{-2}$ Change in volume, $\Delta \mathrm{V}=5 \times 10^{-2} \times 10^{-6} \mathrm{~m}^3$ Bulk modulus, $\mathrm{B}=\frac{\mathrm{P}}{\frac{\Delta \mathrm{V}}{\mathrm{V}}}$ $\begin{aligned} & =\frac{15 \times 10^5 \times 2000 \times 10^{-6}}{5 \times 10^{-8}} \\ & =6 \times 10^{10} \mathrm{Nm}^{-2} \end{aligned}$

Asked in: AP EAMCET 2023 (15 May Shift 2)

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