If both the mass and radius of the earth decrease by `1%` the value of

Options

A. acceleration due to gravity would decrease by nearly `1%`
B. acceleration due to gravity would increase by `1%`
C. escape velocity from the earth's surface would decrease by `1%`
D. the gravitational potential energy of a body on earth's surface will remain unchanged

Answer

B, D

Explanation

The acceleration due to gravity is `g=(GM)/(R^(2))`
The new value of `g` would be
`g'=(G(0.99M))/((0.99R)^(2))=1.01(GM)/(R^(2))`
Thus, `g` woud increase by about `1%`. The new escape velocity would be
`v_(e)=sqrt((2xx0.99MxxG)/(0.99R))=sqrt((2MG)/R)=v_(e)`
Thus, the escape velocity will remain unchanged. The potential energy of a body of mass `m` on the earth's surface would
`-(Gm(0.99M))/((0.99R))=-(GmM)/R`
Thus, the potential energy will also remain unchange. Hence, the correct choices are b and d.