What will be the effect on the value of the acceleration due to gravity on the earth's surface , if the radius of the earth suddenly reduces to half its present value and the mass remains constant ?

Explanation

Let the mass of the earth be M and its radius be R.
Acceleration due to gravity on the earth.s surface, `g=(GM)/(R^2)`
When the radius changes to `R/2` and the mass remains
`g^.=(GM)/(R/2)^2=(4GM)/(R^2)`
`therefore g^. =4g`
Thus, the acceleration due to gravity would be 4 times the present value.