Question

The mass of the earth is $80$ times that of the moon. Their diameters are $12800Km$ and $3200Km$ respectively. The value of g on moon will be _______, if its value on earth is $980cm/s^2$.

• A. $98cm/s^2$
• B. $196cm/s^2$
• C. $100cm/s^2$
• D. $294cm/s^2$

Answer 1

Answer: (B)

$196cm/s^2$

Let $g_e,g_m$ are accelarations due to gravity on earth and moon respectively.
Similarly let $M_e,M_m$ are masses of earth and moon respectively, $r_e,r_m$ are radiuses of earth and moon respectively.
Now, $g_e=\frac{G{M}_e}{r_e^2}$
$g_m=\frac{G{M}_m}{r_m^2}$
taking the ratio, $\frac{g_m}{g_e}=\left(\frac{G{M}_m}{r_m^2}\right)\times \left(\frac{r_e^2}{G{M}_e}\right)$
simplifying and rearranging terms we get
$g_m=\left(\frac{M_m}{M_e}\right)\times {\left(\frac{r_e}{r_m}\right)}^2\times g_e$
Substituting the given values, $g_e=980cm{s}^{-2},$

$Given:\frac{M_e}{M_m}=80,2r_e=128\times {10}^{7}cm,2r_m=32\times {10}^{7}cm$
$g_m=\left(\frac{1}{80}\right)\times {\left(\frac{64\times {10}^7}{16\times {10}^7}\right)}^2\times 980=196cm{s}^{-2}$