Question

if the earth shrinks to 50% of its real radius its mass remaining the same, the weight of a body on the earth will increase or decrease?​

Answer 1

same because gravity remain same

Answer 2

If acceleration due to gravity on earth(g) = G.M/R²,

then weight of the body = mg;

where G is gravitation constant, M is mass of earth and R is the radius.

Now if the radius is reduced by half it means g is reduces by 1/4th because it is inversely proportional to the square of radius.

And weight of the body is directly proportional to g, it will also reduce by a factor of 4.