A satellite is orbiting the Earth with an orb | vedclass

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

Question

(D) Let $M$ be the mass of the Earth,$R$ be the radius of the Earth,and $r$ be the orbital radius of the satellite.The total energy of the satellite a

Vedclass · Accepted Answer

$\sqrt{v_e^2 - 2v_0^2}$

Vedclass · Answer

(D) Let $M$ be the mass of the Earth,$R$ be the radius of the Earth,and $r$ be the orbital radius of the satellite.The total energy of the satellite at distance $r$ is $E_i = -\frac{GMm}{r}$.When it hits the Earth's surface at distance $R$,its potential energy is $U_f = -\frac{GMm}{R}$ and kinetic energy is $K_f = \frac{1}{2}mv^2$.By the law of conservation of energy: $E_i = K_f + U_f$.$-\frac{GMm}{r} = \frac{1}{2}mv^2 - \frac{GMm}{R}$.$\frac{1}{2}mv^2 = \frac{GMm}{R} - \frac{GMm}{r}$.$v^2 = \frac{2GM}{R} - \frac{2GM}{r}$.Since $v_e^2 = \frac{2GM}{R}$ and $v_0^2 = \frac{GM}{r}$,we have $\frac{2GM}{r} = 2v_0^2$.Substituting these,$v^2 = v_e^2 - 2v_0^2$.Therefore,$v = \sqrt{v_e^2 - 2v_0^2}$.

$A$. 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

$A$ satellite is orbiting the Earth with an orbital velocity $v_0$. If it is suddenly stopped and allowed to fall onto the Earth,what will be its velocity when it hits the Earth's surface? (Let $v_e$ be the escape velocity from the Earth's surface.)

Similar Questions

The energy required to take a satellite to a height $h$ above the Earth's surface (radius of Earth $R = 6.4 \times 10^3 \, km$) is $E_1$,and the kinetic energy required for the satellite to be in a circular orbit at this height is $E_2$. The value of $h$ for which $E_1 = E_2$ is:

Two satellites $A$ and $B$,having a ratio of masses $3 : 1$,are in circular orbits of radius $r$ and $4r$ respectively. Calculate the ratio of the total mechanical energy of $A$ and $B$.

For a satellite moving in an orbit around the earth,the ratio of kinetic energy to potential energy 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

An artificial satellite moving in a circular orbit at a distance $h$ from the centre of the Earth has a total energy $E_0$. Then,its potential energy is

Vedclass Test Series

Exam Paper Generator

Online Exam Module