A 2 mW laser operates at wavelength of 500 nm. The number of photons that will be emitted per second is : [Given Planck's constant h = 6.6 × 10^–34 Js, speed of light c = 3.0 × 10⁸ m/s]

The time dependence of the position of a particle of mass m = 2 is given by $$\overrightarrow r \left( t \right) = 2t\widehat i - 3{t^2}\widehat j$$ . Its angular momentum, with respect to the origin, at time t = 2 is

In free space, a particle A of charge 1$$\mu $$C is held fixed at a point P. Another particle B of the same charge and mass 4$$\mu $$g is kept at a distance of 1 mm from P. If B is released, then its velocity at a distance of 9 mm from P is : $$\left[ {Take\,{1 \over {4\pi { \in _0}}} = 9 \times {{10}^9}N{m^2}{C^{ - 2}}} \right]$$

A simple pendulum of length L is placed between the plates of a parallel plate capacitor having electric field E, as shown in figure. Its bob has mass m and charge q. The time period of the pendulum is given by :