Q.Keeping the mass fixed, if the radius of the earth is halved, the acceleration due to gravity at any place will be

Applying the universal law of gravitation to an object of mass m near a large sphere of mass M (like the Earth) at distance r from its centre gives a force $F=GMm/r^2$; dividing by m (Newton's second law, $a=F/m$) gives the acceleration due to gravity, $g=GM/r^2$ -- crucially INDEPENDENT of the falling object's own mass, exactly matching Galileo's experimental finding that all bodies fall at the same rate regardless of mass. Near a planet's surface, $r\approx R$ (the planet's radius), giving the familiar surface value $g=GM/R^2\approx9.8$ m/s^2 for Earth. …