The gravitational pull of the moon is (1/6)^{ | vedclass

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

Question

(B) The acceleration due to gravity $g$ is given by $g = \frac{GM}{R^2}$.Let $g_m, M_m, R_m$ be the gravity,mass,and radius of the moon,and $g_e, M_e,

Vedclass · Accepted Answer

radius of the earth is $(\sqrt{4/3})^{	ext{th}}$ of the moon's radius.

Vedclass · Answer

(B) The acceleration due to gravity $g$ is given by $g = \frac{GM}{R^2}$.Let $g_m, M_m, R_m$ be the gravity,mass,and radius of the moon,and $g_e, M_e, R_e$ be those of the earth.Given: $g_m = \frac{1}{6} g_e$ and $M_m = \frac{1}{8} M_e$.We have the ratio: $\frac{g_m}{g_e} = \frac{M_m}{M_e} 	imes \left(\frac{R_e}{R_m}ight)^2$.Substituting the given values: $\frac{1}{6} = \frac{1}{8} 	imes \left(\frac{R_e}{R_m}ight)^2$.Rearranging gives: $\left(\frac{R_e}{R_m}ight)^2 = \frac{8}{6} = \frac{4}{3}$.Taking the square root: $\frac{R_e}{R_m} = \sqrt{\frac{4}{3}}$.Thus,the radius of the earth is $\sqrt{4/3}$ times the radius of the moon.

The gravitational pull of the moon is $(1/6)^{\text{th}}$ of the earth and the mass of the moon is $(1/8)^{\text{th}}$ of the earth. This implies that the:

Similar Questions

Weight of a body is maximum at

The angular speed of the Earth in $rad/s$,so that bodies on the equator may appear weightless is: [Use $g = 10\, m/s^2$ and the radius of the Earth $R = 6.4 \times 10^3\, km$]

The acceleration due to gravity at a height $1\, km$ above the earth is the same as at a depth $d$ below the surface of earth. Then $d = $ ......... $km$

Acceleration due to gravity is $g$ on the surface of the earth. The value of acceleration due to gravity at a height of $32 \, km$ above the earth's surface is ........ $g$. (Radius of the earth $= 6400 \, km$)

The ratio of the weights of a body on the Earth's surface to that on the surface of a planet is $9 : 4$. The mass of the planet is $\frac{1}{9}^{th}$ of that of the Earth. If $R$ is the radius of the Earth,what is the radius of the planet? (Assume the planets have the same mass density)

Vedclass Test Series

Exam Paper Generator

Online Exam Module