A mass of 5 kg is connected to a spring. The potential energy curve of the simple harmonic motion executed by the system is shown in the figure. A simple pendulum of length 4 m has the same period of oscillation as the spring system. What is the value of acceleration due to gravity on the planet where these experiments are performed?

A capacitor is connected to a 20 V battery through a resistance of 10$$\Omega$$. It is found that the potential difference across the capacitor rises to 2 V in 1 $$\mu$$s. The capacitance of the capacitor is __________ $$\mu$$F. Given : $$\ln \left( {{{10} \over 9}} \right) = 0.105$$

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)