The acceleration due to gravity on the Moon i | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The acceleration due to gravity $g$ at the surface of a planet is given by $g = \frac{GM}{R^2}$.Since mass $M = 	ext{density} (ho) 	imes 	ext

Vedclass · Accepted Answer

$\frac{5}{18}R_e$

Vedclass · Answer

(A) The acceleration due to gravity $g$ at the surface of a planet is given by $g = \frac{GM}{R^2}$.Since mass $M = 	ext{density} (ho) 	imes 	ext{volume} (V) = ho 	imes \frac{4}{3}\pi R^3$,we have $g = \frac{G}{R^2} 	imes ho 	imes \frac{4}{3}\pi R^3 = \frac{4}{3}\pi ho GR$.Therefore,$g \propto ho R$.Taking the ratio for the Moon and Earth: $\frac{g_m}{g_e} = \frac{ho_m}{ho_e} 	imes \frac{R_m}{R_e}$.Given $\frac{g_m}{g_e} = \frac{1}{6}$ and $\frac{ho_e}{ho_m} = \frac{5}{3}$,we have $\frac{ho_m}{ho_e} = \frac{3}{5}$.Substituting these values: $\frac{1}{6} = \frac{3}{5} 	imes \frac{R_m}{R_e}$.Solving for $R_m$: $\frac{R_m}{R_e} = \frac{1}{6} 	imes \frac{5}{3} = \frac{5}{18}$.Thus,$R_m = \frac{5}{18}R_e$.

The acceleration due to gravity on the Moon is $\frac{1}{6}$ times that of the Earth. If the ratio of the density of the Earth $(\rho_e)$ to the Moon $(\rho_m)$ is $\frac{\rho_e}{\rho_m} = \frac{5}{3}$,what is the radius of the Moon $(R_m)$ in terms of the radius of the Earth $(R_e)$?

Similar Questions

When a ball is dropped from a height $h$,it takes $t \ s$ to reach the ground. If the same experiment is done on a different planet having a mass $100$ times the earth's mass and a radius $10$ times the earth's radius,then the time it will take to cover the same height on the new planet is:

The approximate height from the surface of earth at which the weight of the body becomes $\frac{1}{3}$ of its weight on the surface of earth is $.......... \, km$ : [Radius of earth $R = 6400 \, km$ and $\sqrt{3} = 1.732$]

Write the difference between $G$ and $g$.

If the angular speed of the earth is doubled,the value of acceleration due to gravity $(g)$ at the north pole:

$Assertion$ : In a free fall,weight of a body becomes effectively zero.
$Reason$ : Acceleration due to gravity acting on a body having free fall is zero.

Vedclass Test Series

Exam Paper Generator

Online Exam Module