RI Y5 Remedial G-field Assignment

Raffles Institution Physics Department Y5 H2 Physics Term 3 Remedial 1 Chapter 7: Gravitational Field Solving Problems Involving Satellites and Planets 1 Always start with : (a) Gravitational force provides the centripetal force (b) 2 2 GMm mr r  2 Total energy 2 GMm r Kinetic energy 2 GMm r The above two expressions are true for satellites and planets which move in circular orbits. They are not valid for non-orbital motions, such as an asteroid crashing toward the Earth. 1 At a point on the surface of a uniform sphere of diameter d, the gravitational field due to the sphere is X. What would be the corresponding value on the surface of a uniform sphere of the same density but of diameter 2d? A 2X B 4X C 8X D 16X [1981/P2/Q8] 2 Two points P and Q are at distances X and 2X from the centre of a planet respectively. (X is greater than the radius of the planet.) The gravitational potential at P is –800 kJ kg1. When a 1 kg mass is taken from P to Q, the work done on the mass by the gravitational force is A +400 kJ B +200 kJ C 200 kJ D 400 kJ [AJC/08/P1/Q12] 3 A satellite is moved from one circular orbit ar ound the Earth to another circular orbit with a larger orbital radius. As a result of the change, which quantity of the satellite will increase? (i) gravitational force (ii) gravitational potential energy (iii) angular velocity (iv) linear speed A (i) and (iv) B (ii) only C (ii) and (iv) D (iii) and (iv) [TPJC/07/I/11] 4 A satellite skims the Moon’s surface in a circular orbit. The acceleration due to gravity at the Moon’s surface is 6 g and the Moon’s radius is 4 R , where g is the acceleration due to gravity on the surface of the Earth and R is the radius of the Earth. If the satellite skimming the Earth’s surface has a period T, the period of revolution of the Moon’s satellite will be A 2 3 T B 2 3T C 2 2 3 T  D 3 2T [NJC/08/P1/Q15]

Raffles Institution Physics Department Y5 H2 Physics Term 3 Remedial 2 Worked Example (Satellite Motion) 5 A satellite P of mass 2400 kg is placed in a geostationary orbit at a distance of 4.23  107 m from the centre of the Earth. Calculate (a) the angular velocity of the satellite, [2] (b) the speed of the satellite, [2] (c) the acceleration of the satellite, [2] (d) the force of attraction between the Earth and the satellite, [2] (e) the mass of the Earth. [2] [1999/P3/Q2] 6 (a) (i) State in words the relationship between gravitational potential and gravitational field strength. (ii) Explain why gravitational potential has a negative value. (b) The variation of the gravitational potential near a certain planet of radius 10 000 km is shown by the graph in Fig. 2 below. Use the information on the gra