The fractional change in the volume of a glas | vedclass

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Question

(B) The hydraulic pressure $P$ applied to the glass slab is $14 \,atm$. Converting this to Pascals $(Pa)$: $P = 14 	imes 1.013 	imes 10^5 \,Pa \appr

Vedclass · Accepted Answer

$3.54 	imes 10^{-5}$

Vedclass · Answer

(B) The hydraulic pressure $P$ applied to the glass slab is $14 \,atm$. Converting this to Pascals $(Pa)$: $P = 14 	imes 1.013 	imes 10^5 \,Pa \approx 14.182 	imes 10^5 \,Pa$. Given the Bulk modulus $B = 40 	imes 10^9 \,N/m^2$. The formula for Bulk modulus is $B = -\frac{P}{\Delta V/V}$, where $\frac{\Delta V}{V}$ is the fractional change in volume. Therefore, the fractional change in volume is given by: $\frac{\Delta V}{V} = \frac{P}{B}$. Substituting the values: $\frac{\Delta V}{V} = \frac{14 	imes 1.013 	imes 10^5}{40 	imes 10^9} = \frac{14.182 	imes 10^5}{40 	imes 10^9} = 0.35455 	imes 10^{-4} = 3.5455 	imes 10^{-5}$. Rounding to the nearest option, we get $3.54 	imes 10^{-5}$.

The fractional change in the volume of a glass slab when subjected to a hydraulic pressure of $14 \,atm$ is (Bulk modulus of glass $= 40 \times 10^9 \,N/m^2$).

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