A satellite is revolving in a circular orbit at a height h form the earth surface, such that h < < R where R is the earth. Assuming that the effect of earth's atmosphere can be neglected the minimum increase in the speed required so that the satellite could escape from the gravitational field of earth is :

Ice at –20^oC is added to 50 g of water at 40^oC. When the temperature of the mixture reaches 0^oC, it is found that 20 g of ice is still unmelted. The amount of ice added to the water was close to (Specific heat of water = 4.2J/g/^oC Specific heat of Ice = 2.1J/g/^oC Heat of fusion of water at 0^oC= 334J/g)

If the de Broglie wavelength of an electron is equal to the 10^–3 times the wavelength of a photon of frequency 6 $$ \times $$ 10¹⁴ Hz, then the speed of electron is equal to : (Speed of light = 3 $$ \times $$ 10⁸ m/s, Planck's constant = 6.63 $$ \times $$ 10^–34 J.s, Mass of electron = 9.1 $$ \times $$ 10^–31 kg)

A body of mass 1 kg falls freely from a height of 100 m, on a platform mass 3 kg which is mounted on a spring having spring constant k = 1.25 $$ \times $$ 10⁶ N/m. The body sticks to the platform and the spring's maximum compression is found to be x. Given that g = 10 ms^–2 , the value of x will be close to :