Question

7) The acceleration due to gravity on the moon is 1 6 th that on the earth. If the earth and the moon are assumed to have the same density, then the radius of the moon is A) 6Re B) 1/6Re C) 1/3Re D) 1/4Re

Answer 1

SoluTion :-

Given that,

The acceleration due to gravity on the moon is only one sixth that of earth

$\sf {g_m=\frac{g_E}{6} }$

Now, The acceleration due to gravity on moon

$\sf {g_m=\frac{4}{3} \pi R_{m}G \rho\ ....(I) }$

We know that,

The acceleration due to gravity on earth

$\sf {g_E = \frac{Gm}{R^2}}\\\\\sf {g_E =\frac{G(\frac{4}{3} \pi R^3 \rho )}{R^2} }\\\\\sf {g_E =\frac{4}{3} \pi G R \rho\ .....(II) }$

Now, from equation (II) and (I)

The ratio of the acceleration due to gravity on earth and moon

$\sf {\frac{g_m}{g_E} =\frac{R_m}{R_E} }\\\\\\\sf {\frac{g_E}{6 \times g_E} =\frac{R_m}{R_E} }\\\\\\\\sf {\frac{R_m}{R_E} =\frac{1}{6} }$