Question

(1)
Calculate the value of acceleration due to gravity at height 3 R from the
center of the earth.
​

Answer 1

Answer:

3.27m/s2

Explanation:

A = Gm/(R^2)

A1 = Gm/(3r)^3

= Gm/(R^2)9

= A/9

= 9.81m/s2 ÷ 9

= 3.27m/s2

Answer 2

Acceleration due to gravity decreases with height.

The value of acceleration due to gravity changes with height (ie, altitude). If g′is the acceleration due to gravity at a point, at height h above the surface of earth, then

g′=(R+h)2GM

but,  g=R2GM

∴gg′=(R+h)2GM×GMR2=(R+h)2R2

Here, g′=(R+h)2GM=(R+3R)2GM

  =(4R)2GM=16R2GM

  =16ge

Note: At a depth, value of g also decreases. Its value at centre of earth is zero, value of acceleration due to gravity is maximum at the earth's surface. Also value of acceleration due to gravity increases as we go from equator to the pole.

hope this is helpful for u