(1). If R is radius of the earth ,then Find the energy required to move a body of mass m from an orbit of radius 2R to 3R.

Ans:- 1/6 (mgR)

(2). How much energy must be given to a 100kg of rocket missile to carry it from the surface of earth into free space? Given ,the gravitational constant, G = 6.67 x10^-11 Nm²kg^-2, mass of the earth = 6 x 10²⁴ kg and radius of the earth 6.4 x 10⁶ m.

Ans:- 6.253 x 10⁶

(3). Find the change in gravitational potential energy of a body of mass 50kg, when it is moved from the surface of the earth to a point at height twice the radius of the earth. Given radius of the earth, R = 6.4 x 10⁶ m and acceleration due to gravity, g = 9.8 ms².

Ans:- 2.09 x 10⁹

(4). A body is projected vertically upwards from the surface of the earth so as to reach a height equal to the radius of the earth. Neglecting resistance due to air, calculate the initial speed which should be imparted to the body. Given that mass of the earth = 5.98 x 10² kg ; radius of the earth = 6,400 km and gravitational constant , G = 6.67 x10^-11 Nm²kg^-2.

Ans:- 7.89km s^-1

(5). A body is released at a distance for away from the surface of earth. Calculate its speed, when it is near the surface of the earth. Given, g = 9.8 ms^-2; radius of earth, R = 6.37 x 10⁶ m.

Ans:- 1.117 x 10⁶ m.

(6). The radius of the earth is 6.37 x 10⁶ m, its mean density is 5.5 x 10 3kg m-3 and 6.67 x10^-11 Nm²kg^-2 Calculate the earth’s surface potential.

Ans:- 6.235 x 10⁷ J kg^-1.

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