Physics (AS & A Level) · Feb / March 2016 · Paper 42 · Question 1

force proportional to product of the (two) masses and inversely proportional to the square of their separation either reference to point masses or separation << ‘size’ of masses [2]

gravitational force provides / is the centripetal force GMm / r 2 = mv 2 / r or GMm / r 2 = mrω 2 and v = rω and algebra leading to v = (GM / r) 1 / 2 [2]

1. vA / vB = (rB / rA) 1 / 2 = (2.2 × 1010 / 1.3 × 108) 1 / 2 = 13 (13.0) [2]

2. v = 2πr / T or v ∝ r / T or vT / r = constant TA / TB = (rA / rB) × (vB / vA) = (1.3 × 108 / 2.2 × 1010) × (1 / 13) = 4.5 (4.54) × 10–4 or T 2 = 4π2r 3 / GM or T 2 ∝ r 3 or T 2 / r 3 = constant (C1) TA / TB = (rA 3 / rB 3) 1 / 2 = [(1.3 × 108) 3 / (2.2 × 1010) 3]1 / 2 (C1) = 4.5 (4.54) × 10–4 (A1) [3]

T = 2π / 1.7 ×10–4 = 3.70 × 104 s TB = 3.70 × 104 / 4.54 × 10–4 = 8.1 × 107 s [2]

If identifies TA as TB then 0 / 2