(D) For a satellite orbiting close to the surface of a planet of radius $R$ and density $\rho$,the time period $T$ is given by $T = 2\pi \sqrt{\frac{R

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

(D) For a satellite orbiting close to the surface of a planet of radius $R$ and density $\rho$,the time period $T$ is given by $T = 2\pi \sqrt{\frac{R}{g}}$.Since $g = \frac{GM}{R^2}$ and $M = \rho \cdot \frac{4}{3} \pi R^3$,we have $g = \frac{G \cdot \rho \cdot \frac{4}{3} \pi R^3}{R^2} = \frac{4}{3} G \pi \rho R$.Substituting $g$ into the time period formula: $T = 2\pi \sqrt{\frac{R}{\frac{4}{3} G \pi \rho R}} = 2\pi \sqrt{\frac{3}{4 G \pi \rho}}$.Thus,$T \propto \rho^{-1/2}$.

Class 11 Physics Gravitation Motion of Satellites in Circular Orbits and Planets in Elliptical Orbits

Medium

The time period $T$ of a satellite is related to the density $(\rho)$ of the planet around which it is orbiting close to the surface as:

MHT CET 2022 All MHT CET

A
$T \propto \rho^{1/2}$
B
$T \propto \rho$
C
$T \propto \rho^{-3/2}$
D
$T \propto \rho^{-1/2}$

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Physics Questions

Chapter

Gravitation

Subtopic

Motion of Satellites in Circular Orbits and Planets in Elliptical Orbits

Previous Year

MHT CET 2022 Paper All MHT CET years →

Why can the entire surface of the Earth be viewed with the help of a polar satellite?

Easy

View Solution

Two satellites of mass $50\,kg$ and $100\,kg$ revolve around the earth in circular orbits of radius $9\,R$ and $16\,R$ respectively,where $R$ is the radius of the earth. The ratio of the speeds of the two satellites will be:

Medium

View Solution

Shown are several curves [fig. $(a)$,$(b)$,$(c)$,$(d)$,$(e)$,$(f)$]. Explain with reason,which ones amongst them can be possible trajectories traced by a projectile (neglect air friction).

Medium

View Solution

The relay satellite transmits the $T.V.$ programme continuously from one part of the world to another because its

Easy

View Solution

The mean radius of the earth is $R$,its angular speed on its own axis is $\omega$,and the acceleration due to gravity at the earth's surface is $g$. The cube of the radius of the orbit of a geostationary satellite will be

MediumAIPMT 1992

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

The time period $T$ of a satellite is related to the density $(\rho)$ of the planet around which it is orbiting close to the surface as:

Similar Questions

Why can the entire surface of the Earth be viewed with the help of a polar satellite?

Two satellites of mass $50\,kg$ and $100\,kg$ revolve around the earth in circular orbits of radius $9\,R$ and $16\,R$ respectively,where $R$ is the radius of the earth. The ratio of the speeds of the two satellites will be:

Shown are several curves [fig. $(a)$,$(b)$,$(c)$,$(d)$,$(e)$,$(f)$]. Explain with reason,which ones amongst them can be possible trajectories traced by a projectile (neglect air friction).

The relay satellite transmits the $T.V.$ programme continuously from one part of the world to another because its

The mean radius of the earth is $R$,its angular speed on its own axis is $\omega$,and the acceleration due to gravity at the earth's surface is $g$. The cube of the radius of the orbit of a geostationary satellite will be

Vedclass Test Series

Exam Paper Generator

Online Exam Module