Question

so that weight show that weight of an object on the earth is 1/6 of its weight on the earth given that the mass of the earth is hundred times the mass of the moon and its radius is 4 times that of the Moon ​

Answer 1

Answer:

For moon

F = g×m×M/r² ......eq 1

For earth

F' = g×m×M'/(r')²

In both cases

where g is the gravitational constant

m is the mass of object

But M is mass of moon

and M' is mass of earth

r is radius of moon and r' is the radius of earth.

Given that,

100 M = M'

4 r = r'

Now substituting the above values,

F' = g×m×100M/(4r)² = g×m×100M/16r²

= 100/16 ×gmM/r²

= 1/6 × gmM/r² (approximate)

hence proved