If both the mass and radius of the earth decreases 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(0.99" M"))/((0.99 R)^(2))=1.01(GM)/(R^(2))`
Thus, g would increase by about `1%`. The new escape velocity would be
`v_(e )=sqrt((2xx0.99" M"xxG)/(0.99 R))=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 be
`-(Gm(0.99" M"))/((0.99 R))=-(GmM)/(R )`.
Thus, the potential energy will also remain unchanged. Hence, the correct choice are (b) and (d).