Two point masses and are kept apart on a smooth horizontal line

PHYSICS · Multi-part · A Level · Physics · Fields and their consequences · Fields and their consequences

Problem

Two point masses

M_1 = 20\,\text{kg}

and

M_2 = 5\,\text{kg}

are kept

0.60\,\text{m}

apart on a smooth horizontal line. A small test mass is to be placed somewhere on the line joining the two masses so that it experiences zero net gravitational field. Answer the following questions: (i) Let the test mass be at a distance

x

from the centre of the smaller mass

M_2

. Derive an expression for

x

in terms of

M_1,\,M_2,

and the separation

d = 0.60\,\text{m}

. Keep your algebraic steps explicit. (ii) Calculate the numerical value of

x

for the given data and state clearly from which mass this distance is measured. (iii) Using the value of

x

obtained in part (ii), compute the gravitational potential (take zero at infinity) at that point due to the two masses combined. Take

G = 6.67\times10^{-11}\,\text{N m}^2\text{kg}^{-2}

. Express your answer in J\,kg

^{-1}

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