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The bulk modulus of rubber is 9.1xx10^(8...

The bulk modulus of rubber is `9.1xx10^(8)N//m^(2)`. To what depth a rubber ball be taken in a lake so that its volume is decreased by `0.1%`?

A

550 m

B

350 m

C

273 m

D

183 m

Text Solution

Verified by Experts

The correct Answer is:
D
Bulk modulus `K = V(dP)/(dV) = (dP)/(dV//V)`
where `dP = h rho g = h xx 10^(3) xx 9.8`
`(Delta V)/(V) = 0.2 % = (0.2)/(100) = 2 xx 10^(-3)`
`because K = (dP)/(dV//V)`
`9 xx 10^(8) = (h xx 10^(3) xx 9.8)/(2 xx 10^(-3)) = 4.9 xx 10^(6) xx h`
`:. h = (9 xx 10^(8))/(4.9 xx 10^(6)) = 1.83 xx 10^(2) = 183 m`
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