The acceleration due to gravity, g, is given by
![362_2b9fbbb3-cc15-4503-b5f4-ddec506859cf.png](https://secure.tutorsglobe.com/CMSImages/362_2b9fbbb3-cc15-4503-b5f4-ddec506859cf.png)
where M is the mass of the earth, r is the distance from the center of the earth, and G is the universal gravitational constant.
(a) Show that when r changes by Δr, the change in the acceleration due to gravity, Δg, is given by
![2349_8b133193-ef05-449c-9e06-c8e04c58546e.png](https://secure.tutorsglobe.com/CMSImages/2349_8b133193-ef05-449c-9e06-c8e04c58546e.png)
(b) What is the significance of the negative sign?
(c) What is the percent change in g when moving from sea level to the top of Pike's Peak (4.315 km)? Assume the radius of the earth is 6400 km.