The electric field in an electromagnetic wave is given by \(E =56.5 \sin \omega( t - x / c ) \;NC ^{-1}\). Find the intensity of the wave if it is propagating along \(x-\)axis in the free space. (Given \(\left.\varepsilon_{0}=8.85 \times 10^{-12} \;C ^{2} N ^{-1} m ^{-2}\right)\)

A resistance is shown in the figure. Its value and tolerance are given respectively by

In a Young's double slit experiment, \(16\) fringes are observed in a certain segment of the screen when light of wavelength \(700 \,nm\) is used. If the wavelength of light is changed to \(400 \,nm\), the number of fringes observed in the same segment of the screen would be........

A radar sends an electromagnetic signal of electric field \(\left( E _{0}\right)=2.25\,V / m\) and magnetic field \(\left( B _{0}\right)=1.5 \times 10^{-8}\,T\) which strikes a target on line of sight at a distance of \(3\,km\) in a medium After that, a pail of signal \((echo)\) reflects back towards the radar vitli same velocity and by same path. If the signal was transmitted at time \(t_{0}\) from radar. then after how much time (in  \(\times 10^{-5}\,s\)) echo will reach to the radar?

A light beam is described by \(E=800 \sin \omega\left(t-\frac{x}{c}\right)\) An electron is allowed to move normal to the propagation of light beam with a speed of \(3 \times 10^{7}\;{ms}^{-1}\). What is the maximum magnetic force exerted on the electron ?

An inductance coil has a reactance of \(100\, \Omega\). When an \(AC\) signal of frequency \(1000\, Hz\) is applied to the coil, the applied voltage leads the current by \(45^{\circ}\). The self- inductance of the coil is

The disintegration rate of a certain radioactive sample at any instant is \(4250\) disintegrations per minute.\(10\) minutes later, the rate becomes \(2250\) disintegrations per minute. The approximate decay cons \(.........\min^{-1}\)

For an \(RLC\) circuit driven with voltage of amplitude \(v_m\) and frequency \({\omega _0} = \frac{1}{{\sqrt {LC} }}\) the current exhibits resonance. The quality factor, \(Q\) is given by:

Shown in the figure is a hollow icecream cone (it is open at the top). If its mass is \(M,\) radius of its top, \(R\) and height, \(H\), then its moment of inertia about its axis is

A uniform cable of mass \(‘M’\) and length \(‘L’\) is placed on a horizontal surface such that its \({\left( {\frac{1}{n}} \right)^{th}}\)  part is hanging below the edge of the surface. To lift the hanging part of the cable upto the surface, the work done should be

In the given figure, the value of \(V_{0}\) will be \(.....V\).

The change in the magnitude of the volume of an ideal gas when a small additional pressure \(\Delta P\) is applied at a constant temperature, is the same as the change when the temperature is reduced by a small quantity \(\Delta T\) at constant pressure. The initial temperature and pressure of the gas were \(300\, K\) and \(2\; atm\) respectively. If \(|\Delta T|=C|\Delta P|\) then value of \(C\) in \((K / a t m)\) is......

Two point charges of 1 nC and 2 nC are placed at the two corners of equilateral triangle of side 3 cm. The work done in bringing a charge of 3 nC from infinity to the third corner of the triangle is ________ \(\mu\)J.
(\(\frac{1}{4\pi\epsilon_{0}} = 9 \times 10^{9}\ N.m^{2}/C^{2}\))