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A ball falling in a lake of depth 200 m creates a decrease 0.1% in its volume at the bottom. The bulk modulus of material of ball is?

written 5.6 years ago by teamques10 ★ 68k

•   modified 4.5 years ago

fluid mechanics

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written 5.6 years ago by teamques10 ★ 68k

Data:-

h=200 m, dv=0.1%

To find:- k=?

Solution:-

Increase in pressure on ball

$d_p=W_w\times h$

$=9810\times 200$

$1.96\times 10^6 N/m^2$

Also,

Decrease in volume = 0.1%

$-\frac{dv}{v}=\frac{0.1}{100}$

Bulk Modulus (k)

$k=\frac{dP}{-\frac{dv}{v}}=\frac{1.962\times 10^6}{\frac{0.1}{100}}$

$k=1.962\times 10^9 N/m^2$

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