If R is the radius of the Earth and g is the | vedclass

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

Question

(C) The mass of the Earth $M$ can be expressed in terms of its volume $V$ and mean density $\rho$ as: $M = V \rho = \frac{4}{3} \pi R^3 \rho$ ... $(i)

Vedclass · Accepted Answer

$\frac{3 g}{4 \pi R G}$

Vedclass · Answer

(C) The mass of the Earth $M$ can be expressed in terms of its volume $V$ and mean density $ho$ as: $M = V ho = \frac{4}{3} \pi R^3 ho$ ... $(i)$ The acceleration due to gravity $g$ on the surface of the Earth is given by: $g = \frac{GM}{R^2}$ ... $(ii)$ Substituting the expression for $M$ from equation $(i)$ into equation $(ii)$: $g = \frac{G}{R^2} 	imes \left( \frac{4}{3} \pi R^3 ho ight)$ $g = \frac{4}{3} \pi R G ho$ Rearranging the equation to solve for the mean density $ho$: $ho = \frac{3 g}{4 \pi R G}$

If $R$ is the radius of the Earth and $g$ is the acceleration due to gravity on the Earth's surface,then the mean density of the Earth is:

Similar Questions

Which graph correctly presents the variation of acceleration due to gravity with the distance from the centre of the earth (radius of the earth $= R_E$)?

If the radius of the earth shrinks by $1 \%$,its mass remaining the same,then the acceleration due to gravity on the earth's surface would

The mass and diameter of a planet are twice those of earth. The period of oscillation of a pendulum on this planet will be (if it is a second's pendulum on earth).

How does the rotation of the Earth affect the acceleration due to gravity on its surface?

The gravitational force of the Earth on a rocket at a height $h$ from the surface of the Earth is $\frac{1}{3}$ of the gravitational force on the surface of the Earth. Find the relationship between $h$ and $R_e$ (the radius of the Earth).

Vedclass Test Series

Exam Paper Generator

Online Exam Module