The radii of two planets are respectively R_1 | vedclass

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

Question

(D) The acceleration due to gravity $g$ at the surface of a planet of radius $R$ and density $\rho$ is given by the formula:$g = \frac{GM}{R^2}$Since

Vedclass · Accepted Answer

$g_1:g_2 = R_1\rho_1:R_2\rho_2$

Vedclass · Answer

(D) The acceleration due to gravity $g$ at the surface of a planet of radius $R$ and density $\rho$ is given by the formula:$g = \frac{GM}{R^2}$Since the mass $M$ of a planet can be expressed in terms of its density $\rho$ and volume $V = \frac{4}{3}\pi R^3$ as $M = \rho V = \rho \left(\frac{4}{3}\pi R^3\right)$,Substituting this into the expression for $g$:$g = \frac{G}{R^2} \left(\rho \cdot \frac{4}{3}\pi R^3\right) = \frac{4}{3}\pi G \rho R$Therefore,$g \propto \rho R$.For two planets,the ratio of their accelerations due to gravity is:$\frac{g_1}{g_2} = \frac{\rho_1 R_1}{\rho_2 R_2}$Thus,$g_1:g_2 = R_1\rho_1:R_2\rho_2$.

The radii of two planets are respectively $R_1$ and $R_2$ and their densities are respectively $\rho_1$ and $\rho_2$. The ratio of the accelerations due to gravity at their surfaces is

Similar Questions

If the mass and radius of a planet are double those of the Earth,what will be the acceleration due to gravity on this planet compared to the acceleration due to gravity on Earth?

The average density of the Earth is [ $g$ is acceleration due to gravity]:

$A$ spherical planet far out in space has a mass $M_0$ and diameter $D_0$. $A$ particle of mass $m$ falling freely near the surface of this planet will experience an acceleration due to gravity which is equal to

$A$ 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.)

Vedclass Test Series

Exam Paper Generator

Online Exam Module