13. At what altitude in metre will the acceleration due to gravity be 25% of that at earth’s surface (Given, Radius of earth = R metre) a. 1/4R b. R c. 3/8R d. R/2 About the author Emery
Answer: b is the correct option Force on the body placed on Earth’s surface is F= R 2 GMm But, F=mg hence, mg= R 2 GMm where, variables have their usual meanings. gR 2 =GM Now, force on the body at geo-potential height say h (altitude) where the acceleration due to gravity is 25% of that at the earth’s surface i.e. 100 25g = 4 g Hence, we can write 4 g = (R+h) 2 GM 4 g = (R+h) 2 gR 2 (R+h) 2 =4R 2 Taking roots for both sides we get R+h=2R h=R Reply
Answer:
b is the correct option
Force on the body placed on Earth’s surface is
F=
R
2
GMm
But, F=mg hence,
mg=
R
2
GMm
where, variables have their usual meanings.
gR
2
=GM
Now, force on the body at geo-potential height say h (altitude) where the acceleration due to gravity is 25% of that at the earth’s surface i.e.
100
25g
=
4
g
Hence, we can write
4
g
=
(R+h)
2
GM
4
g
=
(R+h)
2
gR
2
(R+h)
2
=4R
2
Taking roots for both sides we get
R+h=2R
h=R