The moon's radius is 1/4 that of the earth an | vedclass

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

Question

(B) The acceleration due to gravity on the surface of a planet is given by the formula $g = \frac{GM}{R^2}$,where $G$ is the universal gravitational c

Vedclass · Accepted Answer

$g/5$

Vedclass · Answer

(B) The acceleration due to gravity on the surface of a planet is given by the formula $g = \frac{GM}{R^2}$,where $G$ is the universal gravitational constant,$M$ is the mass of the planet,and $R$ is its radius.For the Earth,$g_e = \frac{GM_e}{R_e^2} = g$.For the Moon,$g_m = \frac{GM_m}{R_m^2}$.Given that $M_m = \frac{M_e}{80}$ and $R_m = \frac{R_e}{4}$.Substituting these values into the formula for $g_m$:$g_m = \frac{G(M_e/80)}{(R_e/4)^2} = \frac{G M_e}{80} 	imes \frac{16}{R_e^2} = \frac{16}{80} 	imes \frac{GM_e}{R_e^2}$.Since $\frac{GM_e}{R_e^2} = g$,we get $g_m = \frac{1}{5} g = g/5$.

The moon's radius is $1/4$ that of the earth and its mass is $1/80$ times that of the earth. If $g$ represents the acceleration due to gravity on the surface of the earth,then the acceleration due to gravity on the surface of the moon is:

Similar Questions

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

Obtain an expression for the variation in effective gravitational acceleration $g'$ with latitude due to the Earth's rotation.

$g_e$ and $g_p$ denote the acceleration due to gravity on the surface of the Earth and another planet whose mass and radius are twice that of the Earth. Then:

If the radius of earth shrinks by $2 \%$ while its mass remains the same,the acceleration due to gravity on the earth's surface will approximately:

$T$ is the time period of a simple pendulum on the Earth's surface. Its time period becomes $xT$ when taken to a height $R$ (equal to the Earth's radius) above the Earth's surface. Then,the value of $x$ will be:

Vedclass Test Series

Exam Paper Generator

Online Exam Module