The density of earth increased 4 times and its radius becomes half then our weight will ....

Options

A. be four times its present value
B. be doubled
C. remains same
D. be halved

Answer

B

Explanation

`implies ` weight `W = mg = m((GM_e)/(R_e^2))`
`= ((G)/(R_e^2) xx4/3piR_e^3rho)`
`W = m (4/3 pi R_e) rho " "...(1)`
New weight if the density of earth increased four time and radius becomes half is
`W. = m (4/3 piR_e/2G) 4rho`
`= 2 [m(4/3 piR_e/2G) 4rho`
`= 2 [ m(4/3 pi GR_e) rho] " " ...(2)`
`:. W. = 2W`