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Q.

A solid sphere of radius r made of soft material of bulk modulus K is surrounded by a liquid in 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 (drr), is;

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a

Kamg

b

Ka3mg

c

mg3Ka

d

mgKa

answer is C.

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Detailed Solution

 Bulk modulus = volume stress  volume strain = Force  Area  change in volume  volume 
ΔVV=mgka
 but, volume of sphere V=43πr3
ΔVV=3ΔrrΔrr=13×ΔVV=mg3Ka

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