Question

To What depth must a rubber ball be taken in deep sea so that its volume is decreased y 0.1 %. (The bulk modulus of rubber is `9.8 xx 10^8 Nm^(-2)` , and the density of seac water is `10^3 kg m^(-3).)`

Answer 1

Given, Bulk modulus of rubber `(K) = 9.8 xx 10^(8) N//m^(2)`
Density of sea water `(rho) = 10^(3) kg//m^(3)`
Percentage decrease in volume, `((DeltaV)/(V) xx 100) = 0.1 implies (DeltaV)/(V) = (0.1)/(100)`
`implies" "(DeltaV)/(V) = (1)/(1000)`
Let the rubber ball be taken upto depth h.
`therefore` Change in pressure (p) = `hrhog`
`therefore` Bulk modulus `(K) = |(p)/(DeltaV//V)|=(hrhog)/((DeltaV//V))`
`implies " "h=(Kxx(DeltaV//V))/(rhog)=(9.8xx10^(8)xx(1)/(1000))/(10^(3)xx9.8)=100m`