If two planets have their radii in the ratio | vedclass

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

Question

(D) The acceleration due to gravity $g$ on the surface of a planet is given by $g = \frac{GM}{R^2}$.Since the mass $M$ of a planet can be expressed in

Vedclass · Accepted Answer

$mx : ny$

Vedclass · Answer

(D) The acceleration due to gravity $g$ on the surface of a planet is given by $g = \frac{GM}{R^2}$.Since the mass $M$ of a planet can be expressed in terms of its density $d$ and radius $R$ as $M = \frac{4}{3} \pi R^3 d$,we substitute this into the formula for $g$:$g = \frac{G}{R^2} \left( \frac{4}{3} \pi R^3 d ight) = \frac{4}{3} \pi G R d$.This shows that $g \propto R \cdot d$.Given the ratios of radii $\frac{R_1}{R_2} = \frac{x}{y}$ and densities $\frac{d_1}{d_2} = \frac{m}{n}$,the ratio of the acceleration due to gravity is:$\frac{g_1}{g_2} = \frac{R_1}{R_2} 	imes \frac{d_1}{d_2} = \frac{x}{y} 	imes \frac{m}{n} = \frac{xm}{yn}$.Thus,the ratio is $xm : yn$ or $mx : ny$.

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

Similar Questions

The radius of the earth is $6400 \, km$ and $g = 10 \, m/s^2$. In order that a body of $5 \, kg$ weighs zero at the equator,the angular speed of the earth is

$R$ and $r$ are the radii of the Earth and Moon respectively. $\rho_e$ and $\rho_m$ are the densities of the Earth and Moon respectively. The ratio of the accelerations due to gravity on the surfaces of the Earth and Moon is

If the change in the value of $g$ at a height $h$ above the surface of the earth is the same as at a depth $x$ below it,then (both $x$ and $h$ being much smaller than the radius of the earth)

Write the equation of acceleration due to gravity at a height $h$ from the surface of the Earth,where $h << R_e$.

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:

Vedclass Test Series

Exam Paper Generator

Online Exam Module