A satellite is revolving in a circular orbit at a height h above the surface of the earth of radius R . The speed of the satellite in its orbit is one fourth the escape velocity from the surface of the earth. The relation between h and R is

Question

A satellite is revolving in a circular orbit at a height h above the surface of the earth of radius R . The speed of the satellite in its orbit is one fourth the escape velocity from the surface of the earth. The relation between h and R is (A) h=2R (B) h=3R (C) h=5R (D) h=7R

Tardigrade Admin · Accepted Answer

upsilon0 = (1/4) upsilone √(G M/(. R + h .)) = (1/4) √(2 G M/R) (G M/(. R + h .)) = (1/16) × (2 G M/R) R + h = 8 (. R .) R + h = 8 R 7 R = h

Q. A satellite is revolving in a circular orbit at a height $h$ above the surface of the earth of radius $R$ . The speed of the satellite in its orbit is one fourth the escape velocity from the surface of the earth. The relation between $h$ and $R$ is

$h = 2 R$

$h = 3 R$

$h = 5 R$

$h = 7 R$

$υ_{0} = \frac{1}{4} υ_{e}$
$\frac{GM}{( R + h )} = \frac{1}{4} \frac{2 GM}{R}$
$\frac{GM}{( R + h )} = \frac{1}{16} \times \frac{2 GM}{R}$
$R + h = 8 (R)$
$R + h = 8 R$
$7 R = h$

Q. A satellite is revolving in a circular orbit at a height h above the surface of the earth of radius R . The speed of the satellite in its orbit is one fourth the escape velocity from the surface of the earth. The relation between h and R is

h=2R

h=3R

h=5R

h=7R