Question

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Answer 1

Answer:

$\boxed{\sf Fractional \ change \ in \ volume \ of \ glass \ sphere = 2.73 \times 10^{-5}}$

Given:

Hydraulic pressure (P) = $\sf 1.01 \times 10^6 \ N/m^2 }$

Bulk modulus of glass (B) = $\sf 3.7 \times 10^{10} \ N/m^2 }$

To Find:

Fractional change in volume of glass sphere ($\sf \frac{\Delta V}{V}$)

Explanation:

Formula:

$\boxed{ \bold{\sf B = \frac{P}{\frac{\Delta V}{V} }}}$

$\sf \implies \frac{\Delta V}{V} = \frac{P}{B }$

Substituting values of P & B in the equation:

$\sf \implies \frac{\Delta V}{V} = \frac{1.01 \times {10}^{6} }{3.7 \times {10}^{10} }$

$\sf \implies \frac{\Delta V}{V} = \frac{0.273 \times {10}^{6} }{ {10}^{10} }$

$\sf \implies \frac{\Delta V}{V} =0.273 \times {10}^{6 - 10}$

$\sf \implies \frac{\Delta V}{V} =0.273 \times {10}^{ - 4}$

$\sf \implies \frac{\Delta V}{V} =2.73 \times {10}^{ - 5}$

$\therefore$

Fractional change in volume of glass sphere ($\sf \frac{\Delta V}{V}$ ) = $\sf 2.73 \times 10^{-5}$

Answer 2

Answer:

Hydraulic pressure (P) = $$\sf 1.01 \times 10^6 \ N/m^2 }$$

Bulk modulus of glass (B) = $$\sf 3.7 \times 10^{10} \ N/m^2 }$$

To Find:

Fractional change in volume of glass sphere ($$\sf \frac{\Delta V}{V}$$ )

Explanation:

Formula:

$$\boxed{ \bold{\sf B = \frac{P}{\frac{\Delta V}{V} }}}$$

$$\sf \implies \frac{\Delta V}{V} = \frac{P}{B }$$

Substituting values of P & B in the equation:

$$\sf \implies \frac{\Delta V}{V} = \frac{1.01 \times {10}^{6} }{3.7 \times {10}^{10} }$$

$$\sf \implies \frac{\Delta V}{V} = \frac{0.273 \times {10}^{6} }{ {10}^{10} }$$

$$\sf \implies \frac{\Delta V}{V} =0.273 \times {10}^{6 - 10}$$

$$\sf \implies \frac{\Delta V}{V} =0.273 \times {10}^{ - 4}$$

$$\sf \implies \frac{\Delta V}{V} =2.73 \times {10}^{ - 5}$$

$$\therefore$$

Fractional change in volume of glass sphere ($$\sf \frac{\Delta V}{V}$$ ) = $$\sf 2.73 \times 10^{-5}$$

Explanation:

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