A \(5\, \mu F\) capacitor is charged fully by a \(220\,V\) supply. It is then disconnected from the supply and is connected in series to another uncharged \(2.5\;\mu F\) capacitor. If the energy change during the charge redistribution is \(\frac{ X }{100} \;J\) then value of \(X\) to the nearest integer is\(.....\)

The arm \(P Q\) of a rectangular conductor is moving from \(x=0\) to \(x=2 b\) outwards and then inwards from \(x=2 b\) to \(x=0\) as shown in the figure. A uniform magnetic field perpendicular to the plane is acting from \(x=0\) to \(x=b\). Identify the graph showing the variation of different quantities with distance.

An electric field of \(1000\,V/m\) is applied to an electric dipole at angle of \(45^o\). The value of electric dipole moment is \(10^{-29}\, C.m.\) What is the potential energy of the electric dipole?

The magnetic field of an electromagnetic wave is given by \(\vec B = 1.6 \times {10^{ - 6}}\,\cos \,\left( {2 \times {{10}^7}z + 6 \times {{10}^{15}}t} \right)\left( {2\hat i + \hat j} \right)\frac{{Wb}}{{{m^2}}}\) The associated electric field will be

When the switch \(S\), in the circuit shown, is closed, then the value of current \(i\) will be ................. \(A\)

A cylindrical vessel of \(40\) cm radius is completely filled with water and its capacity is \(528\) dm\(^3\) (dm : decimeter). The vessel is placed on a solid block of exactly same height as vessel. If a small hole is made at \(70\) cm below the top of water level, then horizontal range of water falling on the ground in the beginning is __________ cm.

In the resonance experiment, two air columns (closed at one end) of 100 cm and 120 cm long, give 15 beats per second when each one is sounding in the respective fundamental modes. The velocity of sound in the air column is :

A body takes \(4\, {min}\). to cool from \(61^{\circ} {C}\) to \(59^{\circ} {C}\). If the temperature of the surroundings is \(30^{\circ} {C}\), the time taken by the body to cool from \(51^{\circ} {C}\) to \(49^{\circ} {C}\) is \(....\,min\)

Find the electric field at point \(P\) (as shown in figure) on the perpendicular bisector of a uniformly charged thin wire of length \(L\) carrying a charge \(Q.\) The distance of the point \(P\) from the centre of the rod is \(a=\frac{\sqrt{3}}{2} L\).

A sample of an ideal gas is taken through the cyclic process \(ABCA\) as shown in figure. It absorbs, \(40\,J\) of heat during the part \(A B\), no heat during \(BC\) and rejects \(60\,J\) of heat during \(CA\). \(A\) work \(50\,J\) is done on the gas during the part \(BC\). The internal energy of the gas at \(A\) is \(1560\,J\). The work done by the gas during the part \(CA\) is.............\(J\)

If electronic charge \(e\), electron mass \(m\), speed of light in vacuum \(c\) and Planck 's constant \(h\) are taken as fundamental quantities, the permeability of vacuum \(\mu _0\) can be expressed in units of

Bob of a simple pendulum of length \(l\) is made of iron . The pendulum is oscillating over a horizontal coil carrying direct current. If the time period of the pendulum is \(T\) then