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 $2 : 1$.

Column-$I$	Column-$II$
$(1)$ Maximum value of acceleration due to gravity $g$	$(a)$ At the center of the Earth
$(2)$ Minimum value of acceleration due to gravity $g$	$(b)$ At the poles
$(3)$ Zero value of acceleration due to gravity $g$	$(c)$ At the equator

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

What should be the angular velocity of earth due to rotation about its own axis so that the weight at the equator becomes $(3/5)^{th}$ of its initial value? ($g$ = acceleration due to gravity, $R$ = radius of earth)

Match Column-$I$ with Column-$II$.

Column-$I$ Column-$II$

$(1)$ Maximum value of acceleration due to gravity $g$ $(a)$ At the center of the Earth

$(2)$ Minimum value of acceleration due to gravity $g$ $(b)$ At the poles

$(3)$ Zero value of acceleration due to gravity $g$ $(c)$ At the equator

Two spherical planets $A$ and $B$ have the same mass,but their densities are in a ratio $8:1$. For these planets,the ratio of acceleration due to gravity at the surface of $A$ to its value at the surface of $B$ is:

The highest temperature, density, and pressure on Earth are found:

Select the correct statement out of the following:

Vedclass Test Series

Exam Paper Generator

Online Exam Module