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To what depth must a rubber ball be take...

To what depth must a rubber ball be taken in deep sea so that its volume is decreases by `0.1%` (The bulk modulus of rubber is `9.8xx10^(8) N//m` , and the density of sea water is `10^(3) kg//m^(3))`

A

50

B

100 m

C

150 m

D

200 m

Text Solution

Verified by Experts

The correct Answer is:
B
For the rubber ball, the percentage decrease in volume
`= (DeltaV)/(V) xx 100 = 0.1`
`:. (DeltaV)/(V) = (0.1)/(100) = (1)/(1000) = 10^(-3)`
If the ball is taken to a depth h, then
Change in perssure `dP = rhogh`
and `K = V(dP)/(dV) = (V)/(dV) . (rhogh)`
`:. h = K . ((dV)/(V)) xx (1)/(rhog) = (9.8 xx 10^(8) xx 10^(-3))/(10^(3) xx 9.8) = 100 m`
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