DHS 07 Gravitational Field (Tutorial Solutions)

2024 H2 Physics (9749) Gravitation Field_Tutorial Solution 9749 Physics (2024) Topic 7: Gravitational Field 6 – Tutorial Solution - 1 For Internal Use Only LO Sub-topic Tut Qn a Show an understanding of the concept of a gravitational field as an example of field of force and define gravitational field strength at a point as the gravitational force exerted per unit mass placed at that point. b Recognise the analogy between certain qualitative and quantitative aspects of gravitational and electric fields. c Recall and use Newton's law of gravitation in the form F = Gm1m2 / r2. S1,S2 d Derive, from Newton's law of gravitation and the definition of gravitational field strength, the equation g = GM / r2 for the gravitational field strength of a point mass. e Recall and apply the equation g = GM / r2 for the gravitational field strength of a point mass to new situations or to solve related problems. S3,S4,S7, S8,D1,D2 f Show an understandi ng that near the surface of the Earth g is approximately constant and equal to the acceleration of free fall. g Define potential at a point as the work done per unit mass in bringing a small test mass from infinity to the point. h Solve problems using the equation φ = −GM / r for the gravitational potential in the field of a point mass. S5,S6,S9, D3,D4,D5, D6,D10, D11, D12, D13, D14 i Analyse circular orbits in inverse square law fields by relating the gravitational force to the centripetal acceleration it causes. S10,D7,D9 j Show an understanding of geostationary orbits and their application. D8 Dunman High School (Senior High Physics) Gravitational Field Tutorial Solution

2024 H2 Physics (9749) Gravitation Field_Tutorial Solution 9749 Physics (2024) Topic 7: Gravitational Field 6 – Tutorial Solution - 2 For Internal Use Only No Solution Mark S1 F = 2 (3)(2)G r F1 = 2 (3)(2) (2 ) G r = 2 1 (3)(2) 4   G r = 4 F 1 1 S2 Ans: C On the Earth’s surface, F = 32(5760 10 )× EsGM m - - - - (1) At a height of 144 km, F1 = 32[(5760 144) 10 ]+× EsGM m = 32(5904 10 )× EsGM m - - - - (2) (2) (1) : 1F F = 2 2 5760 5904 = 0.952 ≈ 95%  i.e. less by 5% S3 Ans: C On the surface of the planet at distance R from its centre, gravitational field strength due to the planet = 2 GM R S4 Ans: A g = 2 GM r , is a vector. The g ravitational field strength near Earth is directed towards Earth, which is to the left, represented by a negative value. The gravitational field strength near Moon is directed towards Moon, which is to the right, represented by a positive value. S5 Ans: D If gravitational potential energy is zero at infinity , it is always negative anywhere else, i.e. U =− GMm r . Q is a point further away from the Earth’s centre, hence U at point Q is greater than that at point P. i.e. UQ is less negative than UP. S6 Ans: A From φ =− GM r : at φ = –60 MJ kg−1, r is smaller, i.e. close