(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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