More practice questions

4. Q4. Treating the Earth as a uniform sphere, find the gravitational force on a 1 kg mass halfway to the centre, r = R_E/2, in terms of its weight at the surface.

   Show answerHide answer

   Inside a uniform Earth the force is proportional to r: F = GmM_Er/R_E³. At r = R_E/2 it is half its surface value, mg/2, about 4.9 N for 1 kg.

5. Q5. A planet has twice the Earth’s radius but only a quarter of its mean density. Find its surface gravity.

   Show answerHide answer

   g = (4/3)πGρR is proportional to ρR, so the factor is ¼ × 2 = ½: about 4.9 m s^⁻².

6. Q6. Jupiter has mass 1.90 × 10^²⁷ kg and radius 6.99 × 10^⁷ m. Find g at its cloud tops. Take G = 6.67 × 10^⁻¹¹ N m^² kg^⁻².

   Show answerHide answer

   GM is about 1.267 × 10^¹⁷ m^³ s^⁻² and R^² about 4.886 × 10^¹⁵ m^², so g is about 25.9 m s^⁻², roughly 2.6 times the Earth’s.