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THE gravitational field strength at two different points X and Y are 9.0Nkg∧-1 and 4.0Nkg∧-1 respectively .how to determine the ratio (gravitational potential at X/gravitational potential at Y)?

Question

THE gravitational field strength at two different points X and Y are 9.0Nkg∧-1 and 4.0Nkg∧-1 respectively .how to determine the ratio (gravitational potential at X/gravitational potential at Y)?
THE gravitational field strength at two different points X and Y are 9.0Nkg∧-1 and 4.0Nkg∧-1 respectively .how to determine the ratio (gravitational potential at X/gravitational potential at Y)?

Answers

Gravitational Field Strength #g# is given by the expression

#g=\frac {-GM}{r^{2}}#
where #G = 6.67 xx 10^-11 m^3kg^-1s^-2# and #M# is mass producing the field at a distance #r#

Also Gravitational Potential is given by the expression

#V_{grav}=\frac {-GM}{r}#

We need to find ratio
#="gravitational potential at X"/"gravitational potential at Y"=(\frac {-GM}{R_X})/(\frac {-GM}{R_Y})=R_Y/R_X# .....(1)

Given

#g_X=\frac {GM}{R_X^{2}}=9.0Nkg^-1# .....(2)
#g_Y=\frac {GM}{R_Y^{2}}=4.0Nkg^-1# .....(3)

Dividing (2) by (3)

#R_Y^2/R_X^2=9.0/4.0#
#=>R_Y/R_X=sqrt(9.0/4.0)=3/2=1.5#

is the required ratio.


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