A spherical ball of volume 2000 text{ cm}^3 i | vedclass

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Question

(A) Given:Initial volume,$V = 2000 	ext{ cm}^3 = 2000 	imes 10^{-6} 	ext{ m}^3 = 2 	imes 10^{-3} 	ext{ m}^3$.Change in volume,$\Delta V = 5 	ime

Vedclass · Accepted Answer

$6 	imes 10^{10} 	ext{ Nm}^{-2}$

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(A) Given:Initial volume,$V = 2000 	ext{ cm}^3 = 2000 	imes 10^{-6} 	ext{ m}^3 = 2 	imes 10^{-3} 	ext{ m}^3$.Change in volume,$\Delta V = 5 	imes 10^{-2} 	ext{ cm}^3 = 5 	imes 10^{-2} 	imes 10^{-6} 	ext{ m}^3 = 5 	imes 10^{-8} 	ext{ m}^3$.Pressure,$P = 15 	ext{ atm} = 15 	imes 10^5 	ext{ Nm}^{-2}$.The formula for Bulk modulus $(B)$ is given by:$B = \frac{P}{\left(\frac{\Delta V}{V}ight)} = \frac{P 	imes V}{\Delta V}$Substituting the values:$B = \frac{15 	imes 10^5 	imes 2 	imes 10^{-3}}{5 	imes 10^{-8}}$$B = \frac{30 	imes 10^2}{5 	imes 10^{-8}}$$B = 6 	imes 10^{10} 	ext{ Nm}^{-2}$.

$A$ spherical ball of volume $2000 \text{ cm}^3$ is subjected to a hydraulic pressure of $15 \text{ atm}$. If the change in volume is $5 \times 10^{-2} \text{ cm}^3$,the bulk modulus of the material of the spherical ball is (Given: $1 \text{ atm} = 10^5 \text{ Nm}^{-2}$)

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