An electron of mass \(m\) and a photon have same energy \(E.\) The ratio of de-Broglie wavelengths associated with them is

A solid ball of radius \(R\) has a charge density \(\rho \) given by \(\rho  = {\rho _0}\left( {1 - \frac{r}{R}} \right)\) for \(0 \leq r \leq R\). The electric field outside the ball is

Match List \(- I\) (Experiment performed) with List \(-II\) (Phenomena discovered/associated) and select the correct option from the options given the lists

List \(- I\)	List \(- II\)
\((1)\) Davisson and Genner	\((i)\) Wave nature of electrons
\((2)\) Millikan's oil drop experiment	\((ii)\) Charge of an electron
\((3)\) Rutherford experiment	\((iii)\) Quantisation of energy levels
\((4)\) Franck-Hertz experiment	\((iv)\) Existence of nucleus

This question has Statement \(-1\) and Statement \(-2\) Of the four choices given after the Statements, choose the one that best describes the two Statements Statement \(1\) : No work is required to be done to move a test charge between any two points on an equipotential surface Statement \(2\) : Electric lines of force at the equipotential surfaces are mutually perpendicular to each other

For the given circuit, the power across zener diode is ..... \({mW}.\)

In an ammeter, \(5 \%\) of the main current passes through the galvanometer. If resistance of the galvanometer is G, the resistance of ammeter will be _______.

A cylindrical block of mass M and area of cross section A is floating in a liquid of density \(\rho\) and with its axis vertical. When depressed a little and released the block starts oscillating. The period of oscillation is _________ .

A particle of mass \(\mathrm{m}\) is dropped from a height \(h\) above the ground. At the same time another particle of the same mass is thrown vertically upwards from the ground with a speed of \(\sqrt{2 \mathrm{gh}} .\) If they collide head-on completely inelastically, the time taken for the combined mass to reach the ground, in units of \(\sqrt{\frac{\mathrm{h}}{\mathrm{g}}}\) is

The electric field of a plane electromagnetic wave is given by \(\overrightarrow{ E }= E _{0}(\hat{ x }+\hat{ y }) \sin ( kz -\omega t )\) Its magnetic field will be given by

An electron is allowed to move with constant velocity along the axis of current carrying straight solenoid. \(A.\) The electron will experience magnetic force along the axis of the solenoid. \(B.\) The electron will not experience magnetic force. \(C.\) The electron will continue to move along the axis of the solenoid. \(D.\) The electron will be accelerated along the axis of the solenoid. \(E.\) The electron will follow parabolic path-inside the solenoid. Choose the correct answer from the options given below:

Angle of minimum deviation is equal to the half of the angle of prism in an equilateral prism. The refractive index of the prism is __________.

An object is allowed to fall from a height \(R\) above the earth, where \(R\) is the radius of earth. Its velocity when it strikes the earth's surface, ignoring air resistance, will be :

A convex lens of refractive index \(1.5\) and focal length \(18 cm\) in air is immersed in water. The change in focal length of the lens will be \(...........cm\).\(\left(\right.\) Given refractive index of water \(\left.=\frac{4}{3}\right)\)