Question

A rubber ball of bulk modulus `B` is taken to a depth h of a liquid of density `rho`. Find the fractional change in the radius of the ball.
A. `(delta r)/(r) = (rho gh)/(3B)`
B. `(delta r)/(r) = (rho gh)/(2B)`
C. `(delta r)/(r) = (3rho gh)/(B)`
D. `(delta r)/(r) = (2rho gh)/(B)`

Answer 1

Correct Answer - A
The volumetric strain `(delta v) = - (rho)/(B)`,
where `P = rho gh` Then, `- (delta v)/(v) = (pgh)/(B)`
Since the volume of the sphere is `v = (4)/(3) pi r^(3)`,
We have `(delta v)/(v) = (3delta r)/(r)` Using eqs(i) and (ii)
we have `(delta r)/(r) = (rho gh)/(3B)`