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 crosssection 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, \(\left( {\frac{{dr}}{r}} \right)\) is

Pick an option to check your answer.

Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{{mg}}{{3Ka}}\)

Step-by-step Solution

Detailed explanation

\(\Delta P = \frac{{mg}}{a}\)

\(k = - \frac{{\frac{{mg}}{A}}}{{\frac{{4\pi {r^2}dr}}{{\frac{4}{3}\pi {r^3}}}}}\)

\(\frac{{dr}}{r} = - \frac{{mg}}{{3KA}}\)

Same subject

In connection with the circuit drawn below, the value of current flowing through \(2\, k \Omega\) resistor is ............. \(\times 10^{-4} A\)

JEE Mains 2021 Medium
The two thin coaxial rings, each of radius \('a'\) and having charges \(+{Q}\) and \(-{Q}\) respectively are separated by a distance of \('s'.\) The potential difference between the centres of the two rings is :

JEE Mains 2021 Hard
Light ray incident along a vector \(\vec{AO}\) \((\vec{AO} = 2\hat{i}-3\hat{j})\) emerges out along vector \(\vec{OB}\) \((\vec{OB} = C\hat{i}-4\hat{j})\) as shown in the figure below. The value of \(C\) is ________.

JEE Mains 2026 Hard
A rod of length 5 L is bent right angle keeping one side length as 2 L.

The position of the centre of mass of the system: (Consider \(\mathrm{L}=10 \mathrm{~cm}\))

JEE Mains 2025 Medium
An astronaut takes a ball of mass \(m\) from earth to space. He throws the ball into a circular orbit about earth at an altitude of \(318.5 \mathrm{~km}\). From earth's surface to the orbit, the change in total mechanical energy of the ball is \(x \frac{\mathrm{GM}_e \mathrm{~m}}{21 R_e}\). The value of \(x\) is _______. (take \(R_{\mathrm{e}}=6370 \mathrm{~km}\) )

JEE Mains 2024 Hard
Moment of inertia of a body about a given axis is \(1.5\, kg\, m^2\) Initially the body is at rest. In order to produce a rotational kinetic energy of \(1200\, J\), the angular acceleration of \(20\, rad/s^2\) must be applied about the axis of rotation for a duration of ......... \(\sec\).

JEE Mains 2019 Medium

Explore more questions on app

From JEE Mains

An \(HCl\) molecule has rotational, translational and vibrational motions. If the \(rms\) velocity of \(HCl\) molecules in its gaseous phase is \(\bar v ,\,m\) is its mass and \(k_B\) is Boltzmann constant, then its temperature will be

JEE Mains 2019 Medium
A light wave described by \(E =60 \sin \left(3 \times 10^{15}\right) t + \sin \left(12 \times 10^{15}\right)\) t] (in SI units) falls on a metal surface of work function 2.8 eV . The maximum kinetic energy of ejected photoelectron is (approximately) _________ eV .

JEE Mains 2026 Medium
A metallic conductor of length \(1\; m\) rotates in a vertical plane parallel to east-west direction about one of its end with angular velocity \(5 \;rad / s\). If the horizontal component of earth's magnetic field is \(0.2 \times 10^{-4} \;T\), then emf induced between the two ends of the conductor is .............

JEE Mains 2022 Medium
The workdone in an adiabatic change in an ideal gas depends upon only :

JEE Mains 2025 Easy

Explore more questions on app