The electric flux is \(\phi=\alpha \sigma+\beta \lambda\) where \(\lambda\) and \(\sigma\) are linear and surface charge density, respectively. \(\left(\frac{\alpha}{\beta}\right)\) represents

A thin circular disc of mass \(M\) and radius \(R\) is rotating in a horizontal plane about an axis passing through its centre and perpendicular to its plane with angular velocity \(\omega\). If another disc of same dimensions but of mass \(\mathrm{M} / 2\) is placed gently on the first disc co-axially, then the new angular velocity of the system is _______.

The activity of a radioactive material is \(2.56 \times 10^{-3} \,Ci\). If the half life of the material is \(5\) days, after how many days the activity will become \(2 \times 10^{-5} \,Ci\) ?

In the following \(p-V\) diagram the equation of state along the curved path is given by \((V-2)^2=4\) ap where \(a\) is a constant. The total work done in the closed path is

An insulated copper wire of \(100\) turns is wrapped around a wooden cylindrical core of the crosssectional area \(24\,cm ^2\). The two ends of the wire are connected to a resistor. The total resistance in the circuit is \(12\,\Omega\). If an externally applied uniform magnetic field in the core along its axis changes from \(1.5 T\) in one direction to \(1.5\,T\) in the opposite direction, the charge flowing through a point in the circuit during the change of magnetic field will be \(.........\,mC\).

Heat is supplied to a diatomic gas at constant pressure. Then the ratio of \(\Delta Q : \Delta U : \Delta W\) is _______.

An engine of a train, moving with uniform acceleration, passes the signal-post with velocity \(u\) and the last compartment with velocity \(v\). The velocity with which middle point of the train passes the signal post is

Two point charges \(Q\) each are placed at a distance \(d\) apart. A third point charge \(q\) is placed at a distance \(x\) from mid-point on the perpendicular bisector. The value of \(x\) at which charge \(q\) will experience the maximum \(Coulomb's force\) is ...............

For the given circuit the current through battery of \(6\,V\) just after closing the switch ' \(S\) ' will be\(.......A\).

A parallel beam of monochromatic light of wavelength \(600 \mathrm{~nm}\) passes through single slit of \(0.4 \mathrm{~mm}\) width. Angular divergence corresponding to second order minima would be _______ \(\times 10^{-3} \mathrm{rad}\).

A stationary horizontal disc is free to rotate about its axis. When a torque is applied on it, its kinetic energy as a function of \(\theta ,\) where \(\theta \) is the angle by which it has rotated, is given as \(k\theta ^2.\) If its moment of inertia is \(I\) then the angular acceleration of the disc is