An object of mass is taken from the Earth’s surface to a height such that

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

Problem

An object of mass

m

is taken from the Earth’s surface to a height

h

such that

h \ll R

, where

R

is the Earth’s radius. (i) Using the relation

g_h = g\bigl(1 - 2h/R\bigr)

, derive an expression for the fractional change in the weight of the object. (ii) Hence obtain the percentage decrease in weight in terms of

h

and

R

. (iii) Calculate the height above the Earth’s surface at which the weight of the object decreases by

1\%

, taking

R = 6.4 \times 10^{6}\,\text{m}