Question

If the diameter of the earth becomes two times its present value and it mass remains unchanged then how would the weight of an object on the surface of the earth be affected

Answer 1

if diameter is doubled then radius is also doubled, i.e, the distance of the object from the centre doubles. we know that weight is inversely proportional to the square of the distance, so weight reduces to one fourth its original value

Answer 2

weight= Gm¹m²/R²

if d= 2D

then R=4R

therefore

weight = Gm¹m²/(4R)²

= Gm¹m²/16R²

= 1/16× Gm¹m²/R²

thus our weight will decrease by 16times the weight now