(B) According to Kepler's third law of planetary motion,the square of the time period $T$ is proportional to the cube of the orbital radius $R$,i.e.,$

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

its radius of orbit is $4 \, R$ and orbital velocity is $\frac{v_0}{2}$

(B) According to Kepler's third law of planetary motion,the square of the time period $T$ is proportional to the cube of the orbital radius $R$,i.e.,$T^2 \propto R^3$.Given $T_1 = 2 \, days$,$R_1 = R$,$T_2 = 16 \, days$,and $R_2 = ?$.Using the ratio: $\frac{T_2^2}{T_1^2} = \frac{R_2^3}{R_1^3} \Rightarrow \frac{16^2}{2^2} = \left(\frac{R_2}{R}\right)^3$.$\frac{256}{4} = 64 = \left(\frac{R_2}{R}\right)^3$.Taking the cube root on both sides: $\frac{R_2}{R} = 4$,so $R_2 = 4R$.For orbital velocity $v = \sqrt{\frac{GM}{R}}$,we have $v \propto \frac{1}{\sqrt{R}}$.Therefore,$\frac{v_2}{v_1} = \sqrt{\frac{R_1}{R_2}} = \sqrt{\frac{R}{4R}} = \sqrt{\frac{1}{4}} = \frac{1}{2}$.Thus,$v_2 = \frac{v_1}{2} = \frac{v_0}{2}$.

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

Medium

The time period of an artificial satellite in a circular orbit of radius $R$ is $2 \, days$ and its orbital velocity is $v_0$. If the time period of another satellite in a circular orbit is $16 \, days$,then:

A
its radius of orbit is $4 \, R$ and orbital velocity is $v_0$
B
its radius of orbit is $4 \, R$ and orbital velocity is $\frac{v_0}{2}$
C
its radius of orbit is $2 \, R$ and orbital velocity is $v_0$
D
its radius of orbit is $2 \, R$ and orbital velocity is $\frac{v_0}{2}$

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

If a satellite has to orbit the earth in a circular path every $6 \text{ hrs}$, at what distance from the surface of the earth should the satellite be placed (in $\text{ km}$)? (Radius of earth $R_e = 6400 \text{ km}$)
(Assume $\frac{GM}{4\pi^2} = 8 \times 10^{12} \text{ m}^3\text{s}^{-2}$, where $G$ and $M$ are the gravitational constant and mass of earth, and $10^{1/3} = 2.1$)

EasyTS EAMCET 2019

View Solution

Two small,equal masses are attached by a light rod. This object orbits a planet; the length of the rod is smaller than the radius of the orbit,but not negligible. The rod rotates about its axis in such a way that it remains vertical with respect to the planet. Determine the state of the rod (tension or compression) and the stability of the equilibrium with respect to a small angular perturbation.

Medium

View Solution

$A$ satellite is orbiting just above the surface of the earth with period $T$. If $d$ is the density of the earth and $G$ is the universal constant of gravitation,the quantity $\frac{3 \pi}{G d}$ represents :

MediumNEET 2023

View Solution

$A$ planet is revolving around the Sun as shown in the figure. The radius vectors joining the Sun and the planet at points $A$ and $B$ are $90 \times 10^6 \text{ km}$ and $60 \times 10^6 \text{ km}$,respectively. The ratio of velocities of the planet at the points $A$ and $B$ when its velocities make angles $30^{\circ}$ and $60^{\circ}$ with the major axis of the orbit is:

MediumAP EAMCET 2019

View Solution

If the orbital speed of a body revolving in a circular path near the surface of the earth is $8 \ km s^{-1}$,then the orbital speed of a body revolving around the earth in a circular orbit at a height of $19,200 \ km$ from the surface of the earth is (Radius of the earth $R = 6400 \ km$). (in $km s^{-1}$)

MediumTS EAMCET 2025

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 of an artificial satellite in a circular orbit of radius $R$ is $2 \, days$ and its orbital velocity is $v_0$. If the time period of another satellite in a circular orbit is $16 \, days$,then:

Similar Questions

$A$ satellite is orbiting just above the surface of the earth with period $T$. If $d$ is the density of the earth and $G$ is the universal constant of gravitation,the quantity $\frac{3 \pi}{G d}$ represents :

Vedclass Test Series

Exam Paper Generator

Online Exam Module