The light waves from two coherent sources have same intensity \({I}_{1}={I}_{2}={I}_{0} .\) In interference pattern the intensity of light at minima is zero.What will be the intensity of light at maxima?

In a single slit diffraction pattern, a light of wavelength \(6000\) A is used. The distance between the first and third minima in the diffraction pattern is found to be \(3 \mathrm{~mm}\) when the screen in placed 50 \(\mathrm{cm}\) away from slits. The width of the slit is _______ \(\times 10^{-4} \mathrm{~m}\).

The bob of a simple pendulum has mass \(2\,g\) and a charge of \(5.0\,\mu C\). It is at rest in a uniform horizontal electric field of intensity \(2000\,\frac{V}{m}\). At equilibrium, the angle that the pendulum makes with the vertical is (take \(g = 10\,\frac{m}{{{s^2}}}\))

A rod of length 5 L is bent right angle keeping one side length as 2 L.

The position of the centre of mass of the system: (Consider \(\mathrm{L}=10 \mathrm{~cm}\))

A current through a wire depends on time as \(i =\alpha_{0} t +\beta t ^{2}\) where \(\alpha_{0}=20 A / s\) and \(\beta=8 As ^{-2} .\) Find the charge crossed through a section of the wire in \(15 \,s\) (in \(C\))

A nucleus has mass number \(A_1\) and volume \(V_1\). Another nucleus has mass number \(A_2\) and volume \(V_2\). If relation between mass number is \(A_2=4 A_1\), then \(\frac{V_2}{V_1}=\)_______.

Capacitance of an isolated conducting sphere of radius \(R_{1}\) becomes \(n\) times when it is enclosed by a concentric conducting sphere of radius \(R_{2}\) connected to earth. The ratio of their radii \(\left(\frac{ R _{2}}{ R _{1}}\right)\) is:

The pressure acting on a submarine is \(3 \times 10^{5}\;Pa\) at a certain depth. If the depth is doubled, the percentage increase in the pressure acting on the submarine would be: (Assume that atmospheric pressure is \(1 \times 10^{5} \;Pa\) density of water is \(10^{3}\, kg \,m ^{-3}, g =10 \,ms ^{-2}\) )

A particle is rotating in a circular path and at any instant its motion can be described as \(\theta = \dfrac{5t^4}{40} - \dfrac{t^3}{3}\). The angular acceleration of the particle after \(10\) seconds is _______ rad/s\(^2\).