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1. a) The Moon's gravitational field at its surface id 1.70 Ng-1 and its mean radius is 1.74 x 106 m. Calculate the mass of the Moon and elaborate diagram (b) A rocket reaches a height of 100 m on the Earth. gnoring the effect of air resistance on Earth, and assuming it operates in the same way as the Moon, calculate the height that it would reach on the Moon. Assume the Earth's gravitational field = 9.81 Ng-1 and the Gravitational constant (G) = 6.67 x 10- 11m 3 kg-1 s-2 .2. A gas cylinder with a volume of 0.1 m3 contains Helium at a temperature of 300 K. The pressure of the helium is 1.1 x 105 Pa. Calculate:- (a) The mass of helium in the cylinder ( b) The r.m.. speed of the helium atoms.3. A cylinder contans 0.005 m3 of a gas at 20C and at constant pressure of 100 K Pa. The gas is heated and it pushes back a piston at the end of the cylinder by 20 mm and increases its volume. The pressure of the gas remains unchanged. a) What force does the gas exert at the piston of its area is 1.5 x 10-2 m2 . ( b) How much work is done by the gas as it expands and contracts. ( c) What is the final temperature after the gas has expanded? (The mass of gas and its pressure do not change)