(a(i))[1]
State what the direction of a gravitational field line at a point shows.
(a(ii))[2]
Explain, using gravitational field lines, why the gravitational field close to the Earth’s surface is approximately constant when the height changes by a small amount.
(b)
A large isolated uniform sphere has mass $M$ and radius $R$. Point $P$ is on a straight line through the centre of the sphere, with a variable displacement $x$ from the centre, as shown in Fig. 1.1.
(b(i))[2]
Determine an expression for $Y$ in terms of $M$ and $R$. State any other symbols that you use.
(b(ii))[2]
Explain why, at the surface of the sphere, $g$ always has the opposite sign to $x$.
(b(iii))[3]
Complete Fig. 1.2 to show how $g$ varies with $x$ for values of $x$, up to $\pm 3R$, for which point $P$ is outside the sphere.