The kinetic energy and potential energy of a particle executing simple harmonic motion will be equal, when displacement (amplitude = \(a\)) is

A parallel plate capacitor having capacitance \(12\, pF\) is charged by a battery to a potential difference of \(10\, V\) between its plates. The charging battery is now disconnected and a porcelain slab of dielectric constant \(6.5\) is slipped between the plates. The work done by the capacitor on the slab is.......\(pJ\)

A wire of length \(L\) and radius \(r\) is clamped at one end. If its other end is pulled by a force \(F\), its length increases by \(l\). If the radius of the wire and the applied force both are reduced to half of their original values keeping original length constant, the increase in length will become _______.

Two cells are connected between points \(A\) and \(B\) as shown. Cell \(1\) has emf of \(12\,V\) and internal resistance of \(3\,\Omega\). Cell \(2\) has emf of \(6\,V\) and internal resistance of \(6\,\Omega\). An external resistor \(R\) of \(4\,\Omega\) is connected across \(A\) and \(B\). The current flowing through \(R\) will be \(.............A\).

A coil is placed in a time varying magnetic field. If the number of turns in the coil were to be halved and the radius of wire doubled, the electrical power dissipated due to the current induced in the coil would be: (Assume the coil to be short circuited.)

The two light beams having intensities I and 9I interfere to produce a fringe pattern on a screen. The phase difference between the beams is \(\frac{\pi}{2}\) at point \(P\) and \(\pi\) at point \(Q\). Then the difference between the resultant intensities at \(P\) and \(Q\) will be.......\(I\)

The effect of increase in temperature on the number of electrons in conduction band \(\left( n _{ e }\right)\) and resistance of a semiconductor will be as:

A parallel plate capacitor with plates of area \(1\,m^2\) each, are at a separation of \(0.1\,m.\) If the electric field between the plates is \(100\,N/C,\) the magnitude of charge on each plate

In the circuit shown in the figure, the ratio of the quality factor and the band width is \(.............\) s.

Two sources of light emit X-rays of wavelength \(1\, nm\) and visible light of wavelength \(500\, nm ,\) respectively. Both the sources emit light of the same power \(200\, W\). The ratio of the number density of photons of X-rays to the number densitty of photons of the visible light of the given wavelengths is

A ray of light is incident at an angle of \(60^o\) on one face of a prism of angle \(30^o\) . The emergent ray of light makes an angle of \(30^o\)  with incident ray. The angle made by the emergent ray with second face of prism will be....\(^o\)

A bag is gently dropped on a conveyor belt moving at a speed of \(2\,m / s\). The coefficient of friction between the conveyor belt and bag is \(0.4\) Initially, the bag slips on the belt before it stops due to friction. The distance travelled by the bag on the belt during slipping motion is \(.....m\) [Take \(g=10\,m / s ^{-2}\) ]