Question

At what depth would the value of g be 80% of what it is on the surface of the
earth?

Answer 1

answer : R/5

explanation : we know, g = g0(1 - d/R)....(1)

• where g0 is acceleration due to gravity on the surface of the earth ,
• g is acceleration due to gravity at depth d from the surface of the earth
• and R is the radius of the earth.

a/c to question,

g = 80% of g0

so, g = 80/100 × g0 = 0.8g0

now from equation (1),

0.8g0 = g0(1 - d/R)

⇒0.8 = 1 - d/R

⇒0.8 - 1 = - d/R

⇒- 0.2 = - d/R

⇒d = 0.2R = R/5

hence, at depth R/5 would the value of g be 80% of what is on it is on the surface of the earth.