the gravitational potential energy of a body at a distance r from the centre of the earth is U. its weight at a distance 2r from the centre of the earth is

a) U/r

b) U/2r

c) U/4r

d) U/(r*sqrt 2)

Dear Student ,
Gravitational potential energy , U = GMm / r.
For calculating the weight at distance 2r from centre of earth , we need to get m*g.
But here acceleration due to gravity , g is not equal to 9.8 m/s^-2 .
Calculation of g can be done using the formula :-
g = GM / r²
Therefore, the value of g at a distance of 2r = GM / 4r²
Thus , weight of the body at a distance 2r from the body = mg = GMm / 4r² = U / 4r .

So , option c is correct .