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QJEEM18Ph4e6f: JEE Main 2018 Physics - Class 11 JEEM18Ph4e6f Solution: A solid sphere of radius r made of a soft material of bulk…

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

Multiple Choice Options

  • A mgKa{{mg} \over {Ka}}
  • B Kamg{{Ka} \over {mg}}
  • C Ka3mg{{Ka} \over {3mg}}
  • D mg3Ka{{mg} \over {3Ka}}

Step-by-Step Verified Solution

JEE Main 2018 (Offline) Physics - Properties of Matter Question 238 English Explanation

Because of m mass the extra pressure created is,

Δ\Delta P = mga{{mg} \over a}

And Bulk modulus, β\beta = ΔPΔVV{{\Delta P} \over {{{\Delta V} \over V}}}

Given β\beta = K

∴   \therefore\,\,\, K = mgaΔVV{{{{mg} \over a}} \over {{{\Delta V} \over V}}}

We know volume of sphere,

V = 43πr3{4 \over 3}\pi {r^3}

∴   \therefore\,\,\, dVV{{dV} \over V} = 3 drr{{dr} \over r}

∴   \therefore\,\,\, K = mga3drr{{{{mg} \over a}} \over {3{{dr} \over r}}}

⇒\Rightarrow    \,\,\, drr{{dr} \over r} = mg3Ka{{mg} \over {3Ka}}

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