Physics

Problem

Two point masses

5M

and

M

are separated by a fixed distance

L

. For the unaltered system the position of zero net gravitational field lies at a distance

x_0

from the mass

M

. Suppose the larger mass is reduced to

(1-0.020)\,(5M)

(i.e. a

2\%

decrease) while

M

and

L

remain unchanged. a. (i) Derive an expression for the new distance

x

of the null point from the mass

M

in terms of

x_0

and the fractional change in the larger mass. Retain terms up to first order in the small fractional change and neglect higher powers. b. (ii) Hence find the fractional shift

\dfrac{x - x_0}{x_0}

in the position of the null point and state whether the point shifts towards or away from the larger mass. c. (iii) If

L = 1.00\,\text{m}

and

x_0 = 0.25\,\text{m}

, compute the numerical value of the shift in centimetres.

Browse the problem library