Question

If the acceleration due to gravity g at the earth's surface is $9.8m{s}^{-2}$ and mass of the earth is 80 times that of moon, radius of earth 4 times that of the moon, the value of g at the moon's surface will be approximately equal to?

• A. $4m{s}^{-2}$
• B. $1.96m{s}^{-2}$
• C. $27m{s}^{-2}$
• D. $16m{s}^{-2}$

Answer 1

Answer: (B)

$1.96m{s}^{-2}$

acceleration due to gravity is given by

$g=\frac{GM}{r^2}$

so comparing that with that of moon, we get

$g_{moon}=\frac{G\frac{M}{40}}{(\frac{r}{4}{)}^2}=>\frac{2}{5}g$

$g_{moon}=\frac{2}{5}\times 9.8=1.96$

so best option is option B.