Question

if the earth shrinks 50% of its real radius its mass remaining the same the weight of a body on the earth will

Answer 1

Acceleration must have the gravity g = GM/r2 = 9.8 m/s2

If r reduces by 50%, the new radius becomes r' = 50% of r = 50r/100 = 0.50r

New acceleration due to gravity g' = GM/(0.50r)2

                                                 = GM/(0.98r2 )

                                                 = 1.04 g = 10.19 m/s2

To increase the acceleration due to gravity = 10.19 − 9.8 m/s2

                                                       =  0.39 m/s2

Increase in percentage = 0.39 x 100/9.8 = 3. 97%