Question

If the earth shrinks to 50% of its real its mass remaining the same, the weight of a body on the Earth will be a) Decreases by 50% b) Increases by 50% c) Decreases by 25% d) Increases by 300%
I know you will say d is the answer but on researching I got both c and d as answer just think and answer​

Answer 1

Theory :-

Acceleration due to gravity on any planet of mass M and radius R is

$g=\frac{GM}{R^{2}}$

Calculations :-

Initially, $g_1=\frac{GM}{R^2}}$

Finally, $g_2=\frac{GM}{(R/2)^2}=4(\frac{GM}{R^2} )=4g_1$

So, initially weight on earth, W₁ = mg₁

And, Finally weight on earth, W₂ = mg₂

So, W₂ = m(4g₁)

Hence, change in weight = W₂ - W₁ = 3mg₁ and is increased weight.

And, % increase in weight = $(\frac{3mg_1}{mg_1})$ × $100$

                                           = 300% increase.

Comment :-

I don't know why you think C is also an answer. Pls comment me the

method by which you got C. I will check onto it.

Remarks :-

Hope u liked my solution

Pls mark me as brainliest

Thanks.