Question

what will be the value of g inmassof the earth is dubble and radius is half .

Answer 1

Acceleration due to gravity is equal to Gravitational force exerted on the object divided by the mass of the object.

Gravitational force is proportional to the mass of the earth and inversely proportional to the square of the distance between the centre of object and the centre of earth.

So if mass of Earth becomes double the value of g should also double.

If radius becomes half the value of g should become 4 times of its original value. (Approximately, considering the radius of earth is much bigger than the the distance of object from the surface of earth)

If both these things happen together then the value of g should become 8 times of its current value.

Answer 2

Let Mbe 2M and radius r is r/2

then g=GM/r Square

g=6.67*10to the power -11*2M/(r/2)whole square

g=G*2M/r Square /4

g=G*M/r/2

2g=GM/r

g=underrootGM/r