if i decrease the radius of earth to half. What is the effect on its gravitational force?

Question

anonymous · Answer

According to the Newton's law of gravitation:
$$F = \frac{ GMm}{ R^{2} }$$where G = gravitational constant. 
M = mass of Earth 
m = mass of a body on earth's surface
R = distance between A and B from their centers. 
If the radius of the earth is halved, the gravitational force,
$$F = \frac{ Gm_{1}m_{2}  }{ (\frac{ 1 }{ 2 }R)^{2} } = \frac{ Gm_{1}m_{2}  }{ \frac{ R^{2} }{ 4 } }$$Now, $$F = 4\frac{ GMm }{ R^{2} }$$
Therefore, gravitational force will increase by four times.

anonymous · Answer

thanx bro

anonymous · Answer

you are welcomed...

anonymous · Answer

is it really R^2 in denominator

anonymous · Answer

yup! Force is inversely proportional to square of the distances from their centers.

anonymous · Answer

sorry, i have the formula potential diffrence in my mind.
V=GMm/R

anonymous · Answer

its okay...