If the accelaeration due to gravity g at the earth's surface is 9.8 `ms^-2` and mass of earth is 80 times that of moon and radius of earth 4 times that of moon , the value of g at the moon's surface will be

Options

A. `1.96 ms^-2`
B. `2.96ms^-2`
C. `0.96ms ^-2`
D. `3.96 ms ^-2`

Answer

A

Explanation

Accelration due to gravity at earth, `g_e=(GM_e)/(R_e^2)`
Accerleration due to gravity at moon is , `g_e = (GM_m)/(R_m^2)`
Since . M_e = 80M_m and R_e =4R_m
`Rightarrow g e=((G(80Mm))/(4R_m))^2`
= `(80 GM_m)/ (16R_m^2)`

5 `(GM_m)/(R_m^2)`
` g_e= 5g_m
g_e= (g_e)/(5)`
= `(9.8)/5`
`g-m =1,96ms^-2`