If the radius of the earth suddenly decreases to `80%` of its present value, the mass of the earth remaining the same, the value of the acceleration due to gravity will

Options

A. remain unchanged
B. become `9.8//0.32m//s^(2)`
C. become by about `36%`
D. increase by about `56%`

Answer

d

Explanation

`R'=0.8R,` the value of g becomes
`(g_(2))/(g_(1))=(R_(1)^(2))/(R_(2)^(2))=(100)/(64)`
`(g_(2))/(g_(1))=1+(36)/(64)" "therefore (g_(2))/(g_(1))-1=(36)/(64)`
`therefore (g_(2)-g_(1))/(g_(1))=0.56`