Acceleration due to gravity at the surface of | vedclass

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

Question

(B) The acceleration due to gravity $g$ at the surface of a body of radius $R$ and density $\rho$ is given by:$g = \frac{GM}{R^2} = \frac{G(\rho \cdot

Vedclass · Accepted Answer

$\frac{2}{3} R$

Vedclass · Answer

(B) The acceleration due to gravity $g$ at the surface of a body of radius $R$ and density $\rho$ is given by:$g = \frac{GM}{R^2} = \frac{G(\rho \cdot \frac{4}{3}\pi R^3)}{R^2} = \frac{4}{3} \pi G \rho R$Given that $g_p = g_e$ and $\rho_p = 1.5 \rho_e = \frac{3}{2} \rho_e$.Equating the gravity expressions for the planet and the Earth:$\frac{4}{3} \pi G \rho_p R_p = \frac{4}{3} \pi G \rho_e R_e$$\rho_p R_p = \rho_e R_e$Substituting $\rho_p = \frac{3}{2} \rho_e$ and $R_e = R$:$(\frac{3}{2} \rho_e) R_p = \rho_e R$$R_p = \frac{2}{3} R$Thus,the radius of the planet is $\frac{2}{3} R$.

Acceleration due to gravity at the surface of a planet is equal to that at the surface of the Earth,and its density is $1.5$ times that of the Earth. If the radius of the Earth is $R$,the radius of the planet is:

Similar Questions

The depth $d$ at which the value of acceleration due to gravity becomes $\frac{1}{n-1}$ times the value at the earth's surface is ($R=$ radius of the earth).

Imagine a new planet having the same density as that of the earth, but it is two times bigger than the earth in size (radius). If the acceleration due to gravity on the surface of the new planet is $g'$ and that on the surface of the earth is $g$, then:

If two planets have their radii in the ratio $x: y$ and densities in the ratio $m: n$,then the ratio of the acceleration due to gravity on them is

The height in terms of radius of the earth $(R)$, at which the acceleration due to gravity becomes $g/9$, where $g$ is acceleration due to gravity on earth's surface, is . . . . . . .

The ratio of gravitational acceleration at height $3R$ to that at height $4R$ from the surface of the earth is (where $R$ is the radius of the earth):

Vedclass Test Series

Exam Paper Generator

Online Exam Module