Question

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

Answer 1

║⊕ANSWER⊕║

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

Let M be the mass of earth and R be the radius,

we know , $g = \frac{GM}{R^{2} }$

so, if diameter is doubled i.e. d' = 2d which means R' = d = 2R

⇒ g' = $\frac{GM}{4R^{2} }$ = $\frac{g}{4}$

so g becomes g/4.

Also Weight=Mass of object*g

W'=(mass of object*g)/4

That is the weight becomes 1/4.