Mechanical Properties of Solids

JEE Main level, single correct, medium

100 of 118

Question 100 of 118

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 aa 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 (drr)\left(\dfrac{dr}{r}\right) , is:

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Answer: (D) mg3Ka\dfrac{mg}{3Ka}

For sphere,∨=43πr3∨=\dfrac{4}{3}\pi {r}^{3}⇒∆∨∨=3∆rr\Rightarrow \dfrac{∆∨}{∨}=3\dfrac{∆r}{r}⇒P=KΔVV\Rightarrow P=K\dfrac{\Delta V}{V}
⇒P=3K(ΔRR)\Rightarrow P=3K\left(\dfrac{\Delta R}{R}\right)⇒mg3Ka=(ΔRR)\Rightarrow \dfrac{mg}{3Ka}=\left(\dfrac{\Delta R}{R}\right).

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