A student claims that the decrease in the weight of a body at a depth of below the…

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

Problem

A student claims that the decrease in the weight of a body at a depth of

2\,\text{km}

below the Earth’s surface is the same as the decrease at an altitude of

2\,\text{km}

above the surface. Examine this claim. (i) State the relation of the acceleration due to gravity with depth

d

below the surface and with altitude

h

above the surface, valid when

d,\,h \ll R

. (ii) Using these relations, calculate the fractional change in

g

at a depth of

2\,\text{km}

and at an altitude of

2\,\text{km}

, taking

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

. (iii) On the basis of your results, decide whether the student’s claim is correct and give a physical explanation for the trend you obtain.