Let a body of mass be taken first to a small depth below Earth’s surface and then to…
PHYSICS · Multi-part · A Level · Physics · Fields and their consequences · Fields and their consequences
Problem
Let a body of mass m be taken first to a small depth d below Earth’s surface and then to a small altitude h above the surface. Neglect higher-order terms in d/R and h/R throughout.
Answer the following.
(i) Derive an expression that relates h and d when the magnitudes of the fractional decreases in the body’s weight at the two positions are equal.
(ii) Using the result of part (i), find the altitude that produces the same percentage decrease in weight as a depth of 50km.
(iii) If m=5kg, calculate the numerical value of the weight of the body at both positions, taking g=9.8ms−2.
(iv) Comment on how the ratio h/d would change if the approximations used were not limited to the first-order terms.