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A solid sphere of radius r made of a soft material of bulk modulus K is surrounded by a liquid in a cylindrical container. A massless piston of area a floats on the surface of the liquid, covering entire cross section of cylindrical container. When a mass m is placed on the surface of the piston to compress the liquid, the fractional decrement in the radius of the sphere, $d r r$ , is

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mg 3 Ka

Ka 3 mg

Ka mg

mg Ka

answer is B.

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Detailed Solution

$K = dp (− dv / v)$

$Volume of sphere V = \frac{4 π}{3} r^{3}$

$Decrease in volume of sphere - dV = \frac{4 π}{3} 3 r^{2} dr$

$Pressure P = \frac{F orce}{Area} = \frac{mg}{a}$

Thus, $\frac{dr}{r} = \frac{mg}{3 Ka}$

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