Statement (A) Two artificial satellites revol | vedclass

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

Question

(B) The time period $T$ of a satellite revolving around a planet is given by $T = 2\pi \sqrt{\frac{r^3}{GM}}$. Since both satellites are in the same c

Vedclass · Accepted Answer

$A, B$ are true,$C$ is false

Vedclass · Answer

(B) The time period $T$ of a satellite revolving around a planet is given by $T = 2\pi \sqrt{\frac{r^3}{GM}}$. Since both satellites are in the same circular orbit,their orbital radius $r$ is the same,meaning their time periods are identical. Thus,Statement $(A)$ is true.The orbital velocity $v$ of a satellite is given by $v = \sqrt{\frac{GM}{r}}$. This shows that $v \propto \frac{1}{\sqrt{r}}$,meaning the orbital velocity is inversely proportional to the square root of the radius of the orbit. Thus,Statement $(B)$ is true.The escape velocity $v_e$ from a point at distance $r$ from the center of a planet is given by $v_e = \sqrt{\frac{2GM}{r}}$. Since $r = R + h$ (where $R$ is the radius of the planet and $h$ is the altitude),the escape velocity depends on the altitude $h$. Thus,Statement $(C)$ is false.

Similar Questions

$A$ particle of mass $m$ is dropped from a height $R$ equal to the radius of the earth above the tunnel dug through the earth as shown in the figure. Hence the correct statement is

$A$ star of mass $M$ and radius $R$ is made up of gases. The average gravitational pressure compressing the star due to the gravitational pull of the gases making up the star depends on $R$ as

Two particles,each of mass $m$,are moving in a circle of radius $R$ under the influence of their mutual gravitational attraction. What is their speed?

$Assertion$: Space rockets are usually launched in the equatorial line from west to east.
$Reason$: The acceleration due to gravity is minimum at the equator.

Vedclass Test Series

Exam Paper Generator

Online Exam Module