The minimum energy required to launch a satel | vedclass

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

Question

(D) The total energy of the satellite at the surface of the Earth is $E_i = K_i + U_i = K_i - \frac{G M m}{R}$.At an altitude of $2R$ from the surface

Vedclass · Accepted Answer

$\frac{5 G m M}{6 R}$

Vedclass · Answer

(D) The total energy of the satellite at the surface of the Earth is $E_i = K_i + U_i = K_i - \frac{G M m}{R}$.At an altitude of $2R$ from the surface,the distance from the center of the Earth is $r = R + 2R = 3R$.The orbital velocity $v$ at distance $r = 3R$ is given by $v = \sqrt{\frac{G M}{3R}}$.The total energy at the orbit is $E_f = K_f + U_f = \frac{1}{2} m v^2 - \frac{G M m}{3R} = \frac{1}{2} m \left(\frac{G M}{3R}\right) - \frac{G M m}{3R} = \frac{G M m}{6R} - \frac{G M m}{3R} = -\frac{G M m}{6R}$.By the law of conservation of energy,$E_i = E_f$:$K_i - \frac{G M m}{R} = -\frac{G M m}{6R}$.$K_i = \frac{G M m}{R} - \frac{G M m}{6R} = \frac{5 G M m}{6R}$.

$A$. Potential energy of satellite	$I$. Positive
$B$. Total energy of satellite	$II$. Negative
$C$. Kinetic energy of satellite	$III$. Zero
$D$. Gravitational potential energy of satellite at infinity	$IV$. Infinity

The minimum energy required to launch a satellite of mass $m$ from the surface of the Earth of mass $M$ and radius $R$ into a circular orbit at an altitude of $2R$ from the surface of the Earth is:

Similar Questions

The total energy of a circularly orbiting satellite is

The additional kinetic energy to be provided to a satellite of mass $m$ revolving around a planet of mass $M$ to transfer it from a circular orbit of radius $R_1$ to another of radius $R_2$ $(R_2 > R_1)$ is:

The additional kinetic energy to be provided to a satellite of mass $m$ revolving around a planet of mass $M$,to transfer it from a circular orbit of radius $R_1$ to another of radius $R_2$ $(R_2 > R_1)$ is:

The minimum energy required to launch a satellite of mass $m$ from the surface of a planet of mass $M$ and radius $R$ into a circular orbit at an altitude of $2R$ is

Match the following columns.
$A$. Potential energy of satellite $I$. Positive
$B$. Total energy of satellite $II$. Negative
$C$. Kinetic energy of satellite $III$. Zero
$D$. Gravitational potential energy of satellite at infinity $IV$. Infinity

Vedclass Test Series

Exam Paper Generator

Online Exam Module