Two thin, concentric, hollow spherical shells have radii and and carry uniformly…

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

Problem

Two thin, concentric, hollow spherical shells have radii

R_1

and

R_2

(R_2>R_1)

and carry uniformly distributed masses

M_1

and

M_2

respectively. A point mass

m

is placed on the line joining their centres at a distance

r

from the common centre. (i) Derive an expression for the magnitude of the gravitational force acting on

m

when

r>R_2

. (ii) Show that when

r<R_1

, the net gravitational force acting on the mass

m

is zero. (iii) Taking

R_1 = 0.50\,\text{m},\; R_2 = 1.00\,\text{m},\; M_1 = 5.0\,\text{kg},\; M_2 = 8.0\,\text{kg},\; m = 0.20\,\text{kg}

and

r = 1.50\,\text{m}

, compute the magnitude of the force obtained in part (i).