Physics

Problem

Two point masses of

3\,\text{kg}

and

12\,\text{kg}

are fixed

60\,\text{cm}

apart on a smooth horizontal line. A point

P

lies somewhere on the same line. (i) Derive an expression for the net gravitational field strength

E

P

in terms of its distances

x

from the

3\,\text{kg}

mass and

(0.60\,\text{m}-x)

from the

12\,\text{kg}

mass. (ii) Hence obtain the equation that must be satisfied for

E

to vanish and determine, correct to two significant figures, the distance of the null point from the

3\,\text{kg}

mass. (iii) State clearly whether this null point lies between the two masses or outside their separation and justify your answer.