A hydraulic press can lift \(100\, kg\) when a mass \('m'\) is placed on the smaller piston. It can lift ......... \(kg\) when the diameter of the larger piston is increased by \(4\) times and that of the smaller piston is decreased by \(4\) times keeping the same mass \('m'\) on the smaller piston.

An ideal gas initially at \(0^{\circ} \mathrm{C}\) temperature, is compressed suddenly to one fourth of its volume. If the ratio of specific heat at constant pressure to that at constant volume is \(3 / 2\), the change in temperature due to the thermodynamic process is _____ K.

A small point of mass \(m\) is placed at a distance \(2 R\) from the centre ' \(O^{\prime}\) of a big uniform solid sphere of mass M and radius R . The gravitational force on ' m ' due to M is \(\mathrm{F}_1\). A spherical part of radius \(\mathrm{R} / 3\) is removed from the big sphere as shown in the figure and the gravitational force on m due to remaining part of M is found to be \(\mathrm{F}_2\). The value of ratio \(\mathrm{F}_1: \mathrm{F}_2\) is _______.

The amplitude of magnetic field in an electromagnetic wave propagating along \(y\)-axis is \(6.0 \times 10^{-7}\,T\). The maximum value of electric field in the electromagnetic wave is:

Consider a spherical shell of radius \(R\) at temperature \(T\). The black body radiation inside it can be considered as an ideal gas of photons with internal energy per unit volume\(E=\) \(\frac{U}{V} \propto {T^4}\) and pressure \(P = \frac{1}{3}\left( {\frac{U}{V}} \right)\) If the shell now undergoes an adiabatic expansion the relation between \(T\) and \(R\) is

A particle of mass \(200 \,MeV / c ^{2}\) collides with a hydrogen atom at rest. Soon after the collision the particle comes to rest, and the atom recoils and goes to its first excited state. The initial kinetic energy of the particle (in \(eV\) ) is \(\frac{ N }{4} .\) The value of \(N\) is : (Given the mass of the hydrogen atom to be \(\left.1\, GeV / c ^{2}\right)\)

A radioactive nucleus \(A\) with a half life \(T\), decays into a nucleus \(B.\) At \(t = 0\), there is no nucleus \(B\). At sometime \(t\), the ratio of the number of \(B\) to that of \(A\) is \(0.3\). Then, \(t\) is given by

A potentiometer wire of length \(300\,cm\) is connected in series with a resistance \(780\,\Omega\) and a standard cell of emf \(4\,V\). A constant current flows through potentiometer wire. The length of the null point for cell of emf \(20\,mV\) is found to be \(60\,cm\). The resistance of the potentiometer wire is\(...\Omega\)

A positive charge \('q'\) of mass \('m'\) is moving along the \(+ x\) axis. We wish to apply a uniform magnetic field \(B\) for time \(\Delta t\) so that the charge reverses its direction crossing the \(y\) axis at a distance \(d.\) Then