A body of mass is taken to a height above Earth’s surface (Earth is assumed to be a…

PHYSICS · Multi-part · CBSE · Physics · Gravitation · Gravitation

Problem

A body of mass

m

is taken to a height

h

above Earth’s surface (Earth is assumed to be a sphere of radius

R_E

and mass

M_E

). (i) Starting from Newton’s law of gravitation, derive an expression for the acceleration due to gravity

g_h

at altitude

h

in terms of

g

on the surface and the quantities

R_E

and

h

. (ii) For heights small compared with Earth’s radius (

h \ll R_E

), expand your expression up to the first power of

h/R_E

and hence obtain the approximate fractional change

\Delta g/g

. (iii) Using the result of part (ii), estimate the percentage decrease in

g

at an altitude of

640\,\text{m}

above the surface. Take

R_E = 6.4\times10^6\,\text{m}

and

g = 9.80\,\text{m\,s}^{-2}