A superconducting gravity meter can measure changes in gravity of the order Delt

Question

A superconducting gravity meter can measure changes in gravity of the order Delta g/g = 10^-11 You are hiding behind a tree holding the meter, and your 57 kg friend approaches the tree from the other side. How close to you can your friend get before the meter detects a change in g due to his presence? (Assume that the gravity meter is stationary, and that a person's mass can be considered to be concentrated at their center of gravity.) You are in a hot air balloon and are using the meter to determine the rate of ascent (presumed constant). What is the smallest change in altitude that results in a detectable change in the gravitational field of the Earth?

Explanation / Answer

ge = GMe/Re^2

g = Gm/r^2

Differentiate g(r) and simplify to obtain

dg/dr = -2Gm/r^3

dg/dr = -2/r *(Gm/r^2)

dg/dr = -2g/r

dg/g = -2dr/r

dr = |-1/2 x 10^-11 x 6.4 x 10^6 |

dr = 3.2 x 10^-2 mm = 0.032 mm

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.