Gravitation Part 1

Given, gA=gC
Radius of Earth, R=6400km
Height, h=3200km=‌

R

2

Since, g=‌

GM

R2

where, G is gravitational constant.
∴‌‌gA=‌

GM(OA)

R3

. . . (i)
and gC‌‌=‌

GM

(OC)2

=‌

GM

R+h

‌‌=‌

GM

(R+R∕2)2

=‌

GM

(3R∕2)2

. . . (ii)
According to given information from Eqs. (i) and (ii), we get
⇒‌‌OA‌‌=‌

4

9

R=‌

4

9

×6400
AB‌‌=OB−OA
‌ and ‌‌AB=6400−‌

4

9

×6400
⇒‌‌=6400(1−4∕9)=6400×5∕9
‌ Now, ‌OA:AB=‌

6400×4∕9

5∕9×6400

=‌

4

5

‌ Hence, ‌x=4