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).)`

Options

A. 9m
B. 18 m
C. 90 m
D. 180 m

Answer

C

Explanation

Let h be the depth at which the rubber ball be taken. Then
`P = hog" "….(i)`
By definition of bulk modulus,
`B = - (P)/(Delta V//V)`
The negative sign shown that with increase in pressure, a decrease in volume occurs.
`therefore P = B (DeltaV)/(V)`
Using (i), `hpg = B (DeltaV)/(V) or h = (B)/(pg)(DeltaV)/(V)`
Substituting the given values, we get `h = (9 xx 10^(8) Nm^(-2))/(10^(3) kg m^(-3) xx 10 m s^(-2))((0.1)/(100)) = 90 m`