An electron moving with speed \(v\) and a photon moving with speed \(c,\) have same D-Broglie wavelength. The ratio of kinetic energy of electron to that of photon is -

Five persons \(P_1, P_2, P_3, P_4\) and \(P_5\) recorded object distance (u) and image distance (v) using same convex lens having power +5 D as \((25,96),(30,62)\), \((35,37),(45,35)\) and \((50,32)\) respectively. Identify correct statement

One of the two small circular coils, (none of them having any self- inductance) is suspended with a \(V-\) shaped copper wire, with plane horizontal. The other coil is placed just below the first one with plane horizontal. Both the coils are connected in series with a \(dc\) supply. The coils are found to attract each other with a force. Which one of the following statements is incorrect ?

Two metal plates \((A, B)\) are kept horizontally with separation of \(\left(\dfrac{12}{\pi}\right)\) cm, with plate A on the top. An atomizer jet sprays oil (density \(1.5\) g/cm\(^3\)) droplets of radius \(1\) mm horizontally. All oil droplets carry a charge \(5\) nC. The potentials \(V_A\) and \(V_B\) are required on plates A and B respectively in order to ensure the droplets do not descend. The values of \(V_A\) and \(V_B\) are _______.
(Neglect the air resistance to the droplets and take \(g = 10\) m/s\(^2\))

The volume \(V\) of an enclosure contains a mixture of three gases, \(16\, g\) of oxygen, \(28\, g\) of nitrogen and \(44\, g\) of carbon dioxide at absolute temperature \(T\). Consider \(R\) as universal gas constant. The pressure of the mixture of gases is

A uniform rectangular thin sheet \(ABCD\) of mass \(M\) has length \(a\) and breadth \(b\), as shown in the figure. If the shaded portion \(HBGO\) is cut off, the coordinates of the centre of mass of the remaining portion will be

Magnetic flux (in weber) in a closed circuit of resistance \(20\,\Omega\) varies with time \(t(s)\) as \(\phi=8 t ^{2}-9 t +5\). The magnitude of the induced current at \(t =0.25\,s\) will be \(...mA\)

The electric field and magnetic field components of an electromagnetic wave going through vacuum is described by \(E _{ x }= E _0 \sin ( kz -\omega t )\) \(B _{ y }= B _0 \sin ( kz -\omega t )\) Then the correct relation between \(E_0\) and \(B_0\) is given by

An electron with speed \(v\) and a photon with speed \(c\) have the same \(de-Broglie\) wavelength. If the kinetic energy and momentum of electron are \(E_{ e }\) and \(pe _{ e }\) and that of photon are \(E _{ ph }\) and \(p _{ ph }\) respectively. Which of the following is correct?

The speed of electrons in a scanning electron microscope is \(1 \times 10^{7} \,ms ^{-1}\). If the protons having the same speed are used instead of electrons, then the resolving power of scanning proton microscope will be changed by a factor of: