When a rubber ball is taken to a depth of h m | vedclass

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(C) The bulk modulus $B$ is defined as $B = -\frac{\Delta P}{\Delta V/V}$.Here,the change in pressure $\Delta P$ at depth $h$ is given by $\Delta P =

Vedclass · Accepted Answer

$500$

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(C) The bulk modulus $B$ is defined as $B = -\frac{\Delta P}{\Delta V/V}$.Here,the change in pressure $\Delta P$ at depth $h$ is given by $\Delta P = ho g h$.The fractional change in volume is $\frac{\Delta V}{V} = -0.5\, \% = -0.005$ (the negative sign indicates a decrease in volume).Substituting the values into the formula: $B = -\frac{ho g h}{-0.005}$.Rearranging for $h$: $h = \frac{B 	imes 0.005}{ho g}$.Substituting the given values: $h = \frac{9.8 	imes 10^{8} 	imes 0.005}{10^{3} 	imes 9.8}$.$h = \frac{10^{8} 	imes 0.005}{10^{3}} = 10^{5} 	imes 0.005 = 500 \, 	ext{m}$.Thus,the depth is $500 \, 	ext{m}$.

When a rubber ball is taken to a depth of $h$ meters in deep sea,its volume decreases by $0.5\, \%$. Calculate the depth $h$. (Given: Bulk modulus of rubber $B = 9.8 \times 10^{8} \, \text{N/m}^2$,Density of sea water $\rho = 10^{3} \, \text{kg/m}^3$,$g = 9.8 \, \text{m/s}^2$)

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