AP EAMCET Engineering 21 Sep 2020 Shift 2 Paper

(d) Let a unit mass m is present at a distance x from the earth, where gravitational force is zero.
‌

GmMe

x2

=‌

GmM

(D−x)2

.......(i)
where, Me is mass of earth and M is mass of moon.
Given, Me=81M
∴ From Eq. (i), we have
‌‌

Gm81M

x2

=‌

GmM

(D−x)2

⇒‌

81

x2

=‌

1

(D−x)2

⇒‌‌(‌

9

x

)2=‌

1

(D−x)2

⇒‌

9

x

=‌

1

D−x

⇒‌‌9D−9x=x⇒9D=10x
⇒‌‌x=‌

9D

10