A planet has the same density as that of the | vedclass

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

Question

(D) The acceleration due to gravity at the surface of a planet is given by $g = \frac{GM}{R^2}$.Since $M = V \rho = \frac{4}{3} \pi R^3 \rho$,we can w

Vedclass · Accepted Answer

$2:1$

Vedclass · Answer

(D) The acceleration due to gravity at the surface of a planet is given by $g = \frac{GM}{R^2}$.Since $M = V \rho = \frac{4}{3} \pi R^3 \rho$,we can write $g = \frac{G (\frac{4}{3} \pi R^3 \rho)}{R^2} = \frac{4}{3} \pi G \rho R$.Assuming the radius of the planet is the same as the Earth $(R_p = R_e)$ unless otherwise specified,or evaluating the ratio based on the given constants:Given $\rho_p = \rho_e$ and $G_p = 2G_e$.The ratio of acceleration due to gravity is $\frac{g_p}{g_e} = \frac{\frac{4}{3} \pi G_p \rho_p R_p}{\frac{4}{3} \pi G_e \rho_e R_e}$.Assuming $R_p = R_e$,we get $\frac{g_p}{g_e} = \frac{G_p}{G_e} = \frac{2G_e}{G_e} = 2$.Thus,the ratio is $2:1$.

$A$ planet has the same density as that of the Earth,and the universal gravitational constant $G$ is twice that of the Earth. The ratio of the acceleration due to gravity on the planet to that on the Earth is:

Similar Questions

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

What is the height from the surface of earth,where acceleration due to gravity will be $\frac{1}{4}$ of that of the earth (in $km$)? $(R_E = 6400 \ km)$

The acceleration due to gravity at height $h$ above the earth if $h \ll R$ (radius of earth) is given by

$A$ body weighs $500 \,N$ on the surface of the earth. At what distance below the surface of the earth will it weigh $250 \,N$ (in $\,km$)? (Radius of earth, $R = 6400 \,km$)

$A$ body weighs $500 \, N$ on the surface of the earth. How much would it weigh halfway below the surface of the earth (in $, N$)?

Vedclass Test Series

Exam Paper Generator

Online Exam Module