Exams › JEE Main › Physics

A solid sphere of radius R and bulk modulus K is immersed in a liquid held in a cylindrical vessel. A massless piston of area A rests on the liquid surface. When a mass m is placed on the piston, compressing the liquid, what is the fractional change in the sphere's radius, dR/R?

1. mg/(AK)
2. mg/(3AK)
3. mg/A
4. mg/(3AR)

Correct answer: mg/(3AK)

Solution

The pressure increase mg/A compresses the sphere; since dV/V = dP/K and dR/R = (1/3) dV/V, the radius decreases by mg/(3AK).

Related JEE Main Physics questions

• Select the incorrect statement.
• A steel wire has length l and cross-sectional area A. When a certain load is applied, it elongates by 1 cm. If the same load is now applied to another steel wire made of the same material, having twice the length and half the cross-sectional area, what will be its extension?
• For common metals such as aluminium and copper, which sequence correctly represents the relative magnitudes of the elastic moduli?
• A steel sheet fails under a shear stress of 3.5 × 10⁸ N m⁻². The approximate force required to punch a circular hole of diameter 1 cm through a steel plate 0.3 cm thick is:
• A copper wire of fixed volume V is stretched out to a length l. If a constant force F is applied to this wire and it elongates by Δl, which of the following plots would be a straight line?
• A material has Poisson’s ratio equal to 0.5. When a tensile force is applied to a wire made of this material, its cross-sectional area decreases by 4%. The corresponding percentage increase in its length is:

⚔️ Practice JEE Main Physics free + battle 1v1 →