One mole of an ideal monoatomic gas is compressed isothermally in a rigid vessel to double its pressure at room temperature, \(27\,^oC\).The work done on the gas will be

An electron is released from rest near an infinite non-conducting sheet of uniform charge density ' \(-\sigma\) '. The rate of change of de-Broglie wave length associated with the electron varies inversely as \(\mathrm{n}^{\text {th }}\) power of time. The numerical value of \(n\) is ________.

A ring and a solid sphere rotating about an axis passing through their centers have same radii of gyration. The axis of rotation is perpendicular to plane of ring. The ratio of radius of ring to that of sphere is \(\sqrt{\frac{2}{x}}\). The value of \(x\) is \(.......\)

Two hypothetical planets of masses \(m_1\) and \(m_2\) are at rest when they are infinite distance apart. Because of the gravitational force they move towards each other along the line joining their centres . What is their speed when their separation is \('d'\) ? (Speed of \(m_1\) is \(v_1\) and that of \(m_2\) is \(v_2\) )

Given below are two statements: Statement \((I)\) : When currents vary with time, Newton's third law is valid only if momentum carried by the electromagnetic field is taken into account. Statement \((II)\) : Ampere's circuital law does not depend on Biot-Savart's law. In the light of the above statements, choose the correct answer from the options given below:

A particle of mass \(M\) is moving in a circle of fixed radius \(R\) in such a way that its centripetal acceleration at time \(t\) is given by \(n^2Rt^2\) where \(n\) is a constant. The Power delivered to the particle by the force acting on it, is

Refer to the logic circuit given below. For two inputs \((A=1, B=1)\) and \((A=0, B=1)\), output \((Y)\) will be __________.

Find the ratio of energies of photons produced due to transition of an election of hydrogen atom from its \((i)\) second permitted energy level to the first level, and \((ii)\) the highest permitted energy level to the first permitted level.

In an experiment of measuring the refractive index of a glass slab using travelling microscope in physics lab, a student measures real thickness of the glass slab as \(5.25\,mm\) and apparent thickness of the glass slab at \(5.00\,mm\). Travelling microscope has \(20\) divisions in one \(cm\) on main scale and \(50\) divisions on Vernier scale is equal to \(49\) divisions on main scale. The estimated uncertainty in the measurement of refractive index of the slab is \(\frac{x}{10} \times 10^{-3}\), where \(x\) is \(..............\)

Model a torch battery of length \(l\) to be made up of a thin cylindrical bar of radius \('a'\) and a concentric thin cylindrical shell of radius ' \(b\) ' fille in between with an electrolyte of resistivity \(\rho\) (see figure). If the battery is connected to a resistance of value \(R ,\) the maximum Joule heating in \(R\) will take place for

A finite size object is placed normal to the principal axis at a distance of 30 cm from a convex mirror of focal length 30 cm. A plane mirror is now placed in such a way that the image produced by both the mirrors coincide with each other. The distance between the two mirrors is :

For three vectors \(\vec{A}=(-x \hat{i}-6 \hat{j}-2 \hat{k})\), \(\vec{B}=(-\hat{i}+4 \hat{j}+3 \hat{k})\) and \(\vec{C}=(-8 \hat{i}-\hat{j}+3 \hat{k})\), if \(\overrightarrow{\mathrm{A}} \cdot(\overrightarrow{\mathrm{B}} \times \overrightarrow{\mathrm{C}})=0\), them value of \(\mathrm{x}\) is _______.