In a certain isolated mass distribution the radial dependence of the gravitational…

MATHEMATICS · Subjective · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

In a certain isolated mass distribution the radial dependence of the gravitational field intensity is given by

g(r)=\dfrac{A}{r^{2}}

for

r\ge5R

, and

g(r)=\dfrac{B}{r^{3}}

for

R\le r\le5R

, where

A

and

B

are constants and

R

is a fixed length. (i) By demanding continuity of the field at

r=5R

, obtain the relation between

A

and

B

. (ii) Using the zero of potential at infinity, derive an expression for the potential difference

V(10R)-V(R)

. (iii) If

A=3.2\times10^{14}\,\text{N\,m}^{2}\!\text{/kg}

and

R=6.0\times10^{6}\,\text{m}

, evaluate the numerical value of the potential difference obtained in part (ii).