If the radius of the earth is increased by a | vedclass

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

Question

(B) The acceleration due to gravity on the surface of the earth is given by $g = \frac{GM}{R^2}$.Substituting mass $M = \rho V = \rho \left( \frac{4}{

Vedclass · Accepted Answer

$1/5$

Vedclass · Answer

(B) The acceleration due to gravity on the surface of the earth is given by $g = \frac{GM}{R^2}$.Substituting mass $M = \rho V = \rho \left( \frac{4}{3} \pi R^3 \right)$,we get:$g = \frac{G \rho \frac{4}{3} \pi R^3}{R^2} = \frac{4}{3} G \pi \rho R$.Since $G$,$\pi$,and $\frac{4}{3}$ are constants,we have $g \propto \rho R$.To keep $g$ constant,the product $\rho R$ must remain constant.Let the initial density be $\rho_1$ and radius be $R_1$. Let the final density be $\rho_2$ and radius be $R_2 = 5R_1$.Then,$\rho_1 R_1 = \rho_2 R_2$.$\rho_1 R_1 = \rho_2 (5R_1)$.$\rho_2 = \frac{\rho_1}{5}$.Thus,the density must be changed by a factor of $1/5$.

If the radius of the earth is increased by a factor of $5$,by what factor must its density be changed to keep the value of $g$ the same?

Similar Questions

The linear speed of a particle at the equator of the earth due to its spin motion is $V$. The linear speed of the particle at latitude $30^{\circ}$ is:

The time period of a simple pendulum is $T_1$ when on the Earth's surface and $T_2$ when taken to a height $h = 2R$ above the Earth's surface, where $R$ is the radius of the Earth. The ratio $T_1 : T_2$ is:

Consider Earth to be a homogeneous sphere. Scientist $A$ goes deep down in a mine and scientist $B$ goes high up in a balloon. The value of $g$ measured by

The height at which the weight of a body becomes $\frac{1}{9}$ of its weight on the surface of the earth (radius of the earth is $R$) is:

$A$ pendulum is oscillating with frequency $n$ on the surface of the Earth. If it is taken to a depth $d = R/3$ below the surface of the Earth,what is the new frequency of oscillation? ($R$ is the radius of the Earth)

Vedclass Test Series

Exam Paper Generator

Online Exam Module