Four particles each of mass M, move along a circle of radius R under the action of their mutual gravitational attraction as shown in figure. The speed of each particle is :

Electric field of plane electromagnetic wave propagating through a non-magnetic medium is given by

E = 20cos(2 $$\times$$ 10¹⁰ t $$-$$ 200x) V/m. The dielectric constant of the medium is equal to : (Take $$\mu$$_r = 1)

There are two infinitely long straight current carrying conductors and they are held at right angles to each other so that their common ends meet at the origin as shown in the figure given below. The ratio of current in both conductor is 1 : 1. The magnetic field at point P is ____________.

The temperature of 3.00 mol of an ideal diatomic gas is increased by 40.0$$^\circ$$C without changing the pressure of the gas. The molecules in the gas rotate but do not oscillate. If the ratio of change in internal energy of the gas to the amount of workdone by the gas is $${x \over {10}}$$. Then the value of x (round off to the nearest integer) is ___________. (Given R = 8.31 J mol^$$-$$1 K^$$-$$1)