Question

how can we mathematically prove that weight of an object on moon is 1/6th of its weight on earth???? plz help

Answer 1

hell...ooo


Suppose a body of mass m and its weight on the moon is Wm (where W is the weight and m is the moon;which means weight on the moon).Mass of the moon is M
and its radius is R

Weight of an object on the moon =
F with which the moon pulls.

Wm = GM*m/r2

Weight of the same object on the earth is W

Mass of the earth is 100 times of that of the moon.

Radius of the moon = R

Radius of the Earth = 4R

Weight of the object on the moon = 

We = G100M*m/(4R)2

We = G100M*m/(16R)2
Wm/We =G * M * m * 16R2/R2 * g * 100M * m 

=16/100

Wm/We = 16/100 =1/6

Weight on the moon is 1/6 weight on the earth

Answer 2

Wm = GM*m/r2

Weight of the same object on the earth is W

Mass of the earth is 100 times of that of the moon.

Radius of the moon = R

Radius of the Earth = 4R

Weight of the object on the moon = 

We = G100M*m/(4R)2

We = G100M*m/(16R)2
Wm/We =G * M * m * 16R2/R2 * g * 100M * m 

=16/100

Wm/We = 16/100 =1/6