A satellite revolving around the earth at a c | vedclass

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

Question

(B) The acceleration due to gravity $g$ at a height $h$ from the surface of the earth is given by:$g = g_0 \left( \frac{R}{R+h} \right)^2 = \frac{16}{

Vedclass · Accepted Answer

$\frac{343}{16}$

Vedclass · Answer

(B) The acceleration due to gravity $g$ at a height $h$ from the surface of the earth is given by:$g = g_0 \left( \frac{R}{R+h} \right)^2 = \frac{16}{49} g_0$Taking the square root on both sides:$\frac{R}{R+h} = \frac{4}{7}$$7R = 4R + 4h \implies 4h = 3R \implies h = \frac{3R}{4}$The orbital radius $r$ is:$r = R + h = R + \frac{3R}{4} = \frac{7R}{4}$The time period $T$ of a satellite is given by:$T = 2\pi \sqrt{\frac{r^3}{GM}}$Squaring both sides:$T^2 = \frac{4\pi^2 r^3}{GM} = \frac{4\pi^2}{GM} \left( \frac{7R}{4} \right)^3 = \frac{4\pi^2}{GM} \left( \frac{343 R^3}{64} \right) = \frac{343}{16} \left[ \frac{\pi^2 R^3}{GM} \right]$Comparing this with $K \left[ \frac{\pi^2 R^3}{GM} \right]$,we get $K = \frac{343}{16}$.

Similar Questions

The mean radius of Earth is $R$,and its angular speed on its axis is $\omega$. What will be the radius of orbit of a geostationary satellite?

$A$ planet is moving in a circular orbit. It completes $2$ revolutions in $360$ days. What is its angular frequency?

The distances of two planets $A$ and $B$ from the sun are $r_A$ and $r_B$ respectively. Given that $r_B = 100 r_A$. If the orbital speed of planet $A$ is $v$,then the orbital speed of planet $B$ is:

The radii of circular orbits of two satellites $A$ and $B$ of the earth are $4R$ and $R,$ respectively. If the speed of satellite $A$ is $3V,$ then the speed of satellite $B$ will be ...... $V$.

The rotation period of an earth satellite close to the surface of the earth is $83$ minutes. The time period of another earth satellite in an orbit at a distance of three earth radii from its surface will be .......... $\min$

Vedclass Test Series

Exam Paper Generator

Online Exam Module