The unit of \(\sqrt{\frac{2 \mathrm{I}}{\epsilon_0 c}}\) is :
(I = intensity of an electromagnetic wave, \(\mathrm{c}:\) speed of light)

For which of the following particles will it be most difficult to experimentally verify the deBroglie relationship?

Correct formula for height of a satellite from earths surface is _______.

Two coils of self inductance \(L _{1}\) and \(L _{2}\) are connected in series combination having mutual inductance of the coils as \(M\). The equivalent self inductance of the combination will be ...............

A body falling under gravity covers two points \(A\) and \(B\) separated by \(80 \mathrm{~m}\) in \(2 \mathrm{~s}\). The distance of upper point A from the starting point is________ \(\mathrm{m}\) (use \(\mathrm{g}=10 \mathrm{~ms}^{-2}\) )

A tiny metallic rectangular sheet has length and breadth of 5 mm and 2.5 mm , respectively. Using a specially designed screw gauge which has pitch of 0.75 mm and 15 divisions in the circular scale, you are asked to find the area of the sheet. In this measurement, the maximum fractional error will be \(\frac{x}{100}\) where \(x\) is _________.

The acceleration due to gravity on the surface of earth is \(g\). If the diameter of earth reduces to half of its original value and mass remains constant, then acceleration due to gravity on the surface of earth would be :

A sinusoidal voltage of peak value \(283\, V\) and angular frequency \(320/s\) is applied to a series \(LCR\) circuit. Given that \(R\, = 5\,\Omega \) , \(L\,= 25\, mH\) and \(C\, = 1000\, \mu F\). The total impedance, and phase difference between the voltage across the source and the current will respectively be

Which of the following equations is dimensionally incorrect? Where \(t=\) time, \(h=\) height, \(s=\) surface tension, \(\theta=\) angle, \(\rho=\) density, \(a, r=\) radius, \(g=\) acceleration due to gravity, \({v}=\) volume, \({p}=\) pressure, \({W}=\) work done, \(\Gamma=\) torque, \(\varepsilon=\) permittivity, \({E}=\) electric field, \({J}=\) current density, \({L}=\) length.

A wedge of mass \(M = 4\,m\) lies on a frictionless plane. A particle of mass \(m\) approaches the wedge with speed \(v\). There is no friction between the particle and the plane or between the particle and the wedge. The maximum height climbed by the particle on the wedge is given by

Two materials having coefficients of thermal conductivity \(3K\) and \(K\) and thickness \(d\) and \(3d\), respectively, are joined to form a slab as shown in the figure. The temperatures of the outer surfaces are  \(\theta_2\) and \(\theta_1\) respectively  \(\left( {\theta _2} > {\theta _1} \right)\) . The temperature at the interface is

A transistor is used in an amplifier circuit in common emitter mode. If the base current changes by \(100 \,\mu A\), it brings a change of \(10 \,mA\) in collector current. If the load resistance is \(2 \,k \Omega\) and input resistance is \(1 \,k \Omega\), the value of power gain is \(x \times 10^{4}\). The value of \(x\) is_________