The masses of two planets are in the ratio 1 | vedclass

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

Question

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

Vedclass · Accepted Answer

$2 : 1$

Vedclass · Answer

(B) The acceleration due to gravity $g$ on the surface of a planet is given by the formula $g = \frac{GM}{R^2}$,where $M$ is the mass of the planet and $R$ is its radius.Let the masses of the two planets be $M_1$ and $M_2$,and their radii be $R_1$ and $R_2$.Given: $\frac{M_1}{M_2} = \frac{1}{2}$ and $\frac{R_1}{R_2} = \frac{1}{2}$.The ratio of the acceleration due to gravity is $\frac{g_1}{g_2} = \frac{M_1}{M_2} 	imes (\frac{R_2}{R_1})^2$.Substituting the given values: $\frac{g_1}{g_2} = \frac{1}{2} 	imes (\frac{2}{1})^2 = \frac{1}{2} 	imes 4 = \frac{2}{1}$.Therefore,the ratio is $2 : 1$.

The masses of two planets are in the ratio $1 : 2$. Their radii are in the ratio $1 : 2$. The ratio of the acceleration due to gravity on the planets is:

Similar Questions

If the radius of the Earth were to shrink by half,its mass remaining the same,what would be the weight of an object on its surface?

$A$ body weighs $300 \ N$ on the surface of the earth. How much will it weigh at a distance $\frac{R}{2}$ below the surface of the earth (in $N$)? ($R$ is the radius of the earth.)

The acceleration due to gravity at an altitude $h$ above the Earth's surface is half of its value on the surface of the Earth. If the radius of the Earth $R = 4000 \ mile$,the altitude $h$ is approximately ......... $mile$.

What should be the angular speed with which the Earth must rotate on its axis so that a person on the equator would weigh $\frac{3}{5}$ th as much as their present weight?

At which location on Earth is the value of $g$ maximum? State the reasons.

Vedclass Test Series

Exam Paper Generator

Online Exam Module