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  • If a rubber cube is taken deep in a lake, its volume reduces by <img alt="0.5 \%." src="h

If a rubber cube is taken 50 \mathrm{~m} deep in a lake, its volume reduces by 0.5 \%. The bulk modulus of rubber is nearly.

Option: 1

\mathrm{10^6 \mathrm{~Pa}}


Option: 2

\mathrm{10^7 \mathrm{~Pa}}


Option: 3

\mathrm{10^8 \mathrm{~Pa}}


Option: 4

\mathrm{10^9 \mathrm{~Pa}}


Answers (1)

Excess pressure at depth \mathrm{h=50 \mathrm{~m}} is

\mathrm{ P=h \rho g=50 \times 1000 \times 9.8=4.9 \times 10^5 \mathrm{~Pa} }
Volume strain \mathrm{\frac{\Delta V}{V}=-0.5 \%=-0.5 \times 10^{-2}}
\mathrm{ \therefore \quad \text { Bulk modulus }=-\frac{P}{\frac{\Delta V}{V}}=-\frac{4.9 \times 10^5}{-0.5 \times 10^{-2}}=10^8 \mathrm{~Pa} }
So the correct choice is (c).

Posted by

Kshitij

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