Physics (AS & A Level) · May / June 2016 · Paper 42 · Question 1
9702
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A binary star consists of two stars A and B that orbit one another, as illustrated in Fig. 1.1. 2.8 × 108 km t t G 3 VWDU % PDVV 0% VWDU $ PDVV 0$ Fig. 1.1 The stars are in circular orbits with the centres of both orbits at point P, a distance d from the centre of star A.
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1(a)(i)[2]
gravitational force provides/is the centripetal force same gravitational force (by Newton III) [2]
1(a)(ii)[2]
ω = 2π / T = 2π / (4.0 × 365 × 24 × 3600) = 5.0 (4.98) × 10–8 rad s–1 [2]
1(b)(i)[3]
(centripetal force =) MAdω2 = MB(2.8 × 108 –d)ω2 or MAdA = MBdB MA / MB = 3.0 = (2.8 × 108 – d) / d d = 7.0 × 107 km [3]
1(b)(ii)[3]
GMAMB / (2.8 × 1011) 2 = MAdω2 MB = (2.8 × 1011) 2 × dω2 / G = (2.8 × 1011) 2 × (7.0 × 1010) × (4.98 × 10–8) 2 / (6.67 × 10–11) = 2.0 × 1029 kg [3]
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