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 acceleration due to gravity $g$ at the Earth's surface is given by the formula:$g = \frac{G M}{R^2}$where $M$ is the mass of the Earth and $G$

Vedclass · Accepted Answer

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

Vedclass · Answer

(C) The acceleration due to gravity $g$ at the Earth's surface is given by the formula:$g = \frac{G M}{R^2}$where $M$ is the mass of the Earth and $G$ is the universal gravitational constant.The mass $M$ of the Earth can be expressed in terms of its mean density $ho$ and radius $R$ as:$M = 	ext{Volume} 	imes 	ext{Density} = \left( \frac{4}{3} \pi R^3 ight) ho$Substituting the expression for $M$ into the formula for $g$:$g = \frac{G}{R^2} 	imes \left( \frac{4}{3} \pi R^3 ho ight)$Simplifying the equation:$g = \frac{4}{3} \pi G R ho$Solving for the density $ho$:$ho = \frac{3 g}{4 \pi G R}$Thus,the correct option is $C$.

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

$A$ uniform rope of mass $0.1 ~kg$ and length $2.45 ~m$ hangs from a rigid support. The time taken by the transverse wave formed in the rope to travel through the full length of the rope is (Assume $g=9.8 ~m/s^2$) (in $~s$)

In a compound,$C$,$H$,and $N$ atoms are present in the ratio $9 : 1 : 3.5$ by weight. The molecular weight of the compound is $108$. Its molecular formula is:

The mean of five observations is $4$ and their variance is $5.2$. If three of these observations are $1, 2$ and $6$,then the other two are

Select incorrect sentence from below.

Which of the following is true for organisms of the same species?

Vedclass Test Series

Exam Paper Generator

Online Exam Module