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A rubber ball of bulk modulus B is taken...

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)`

Text Solution

Verified by Experts

The correct Answer is:
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)`
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Knowledge Check

  • A ball of density rho is released from deep inside of a liquid of density 2 rho . It will move up

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  • The pressure at depth h below the surface of a liquid of density rho open to the atmosphere is

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