KEAM 2021 Physics and Chemistry Solved Paper

Acceleration due to gravity, g=‌

GM

R2

where, R is radius of the earth, M is the mass of the earth and G is gravitational constant.
⇒ g∝‌

M

R2

...... (i) (∵G is constant)
Let new acceleration due to gravity be g, new radius of earth is R′=R/2 and new mass of earth is M′=‌

M

2

Now, g′∝‌

M′

R′2

....(ii)
On dividing Eq. (ii) by Eq. (i), we get
⇒‌‌‌

g′

g

=‌

M′

M

‌

R2

R′2

Given, M′=‌

M

2

and R′=‌

R

2

⇒‌‌‌

g′

g

=‌

M/2

M

‌

(R)2

(R/2)2

or g′=2g