Two identical satellites are at the heights R and 7 R from the earth's surface. Then which of the following statement is incorrect: ( R = Radius of the earth)

Question

Two identical satellites are at the heights R and 7 R from the earth's surface. Then which of the following statement is incorrect: ( R = Radius of the earth) (A) Ratio of total energy of both is 5 (B) Ratio of kinetic energy of both is 4 (C) Ratio of potential energy of both 4 (D) Ratio of total energy of both is 4

Tardigrade Admin · Accepted Answer

TE 1=-( GMm /2( R + R ))=-( GMm /4 R ) TE 2=-( GMm /2( R +7 R ))=-( GMm /16 R ) ( TE 1/ TE 2)=(4/1) ( KE 1/ KE 2)=(-( GMm /4 R )/-( GMm )16 R )=(4/1)

Q. Two identical satellites are at the heights $R$ and $7 R$ from the earth's surface. Then which of the following statement is incorrect :
( $R =$ Radius of the earth)

Ratio of total energy of both is 5

Ratio of kinetic energy of both is 4

Ratio of potential energy of both 4

Ratio of total energy of both is 4

$T E_{1} = - \frac{GM m}{2 ( R + R )} = - \frac{GM m}{4 R}$
$T E_{2} = - \frac{GM m}{2 ( R + 7 R )} = - \frac{GM m}{16 R}$
$\frac{T E _{1}}{T E _{2}} = \frac{4}{1}$
$\frac{K E _{1}}{K E _{2}} = \frac{- \frac{GM m}{4 R}}{- \frac{GM m}{16 R}} = \frac{4}{1}$

Q. Two identical satellites are at the heights R and 7R from the earth's surface. Then which of the following statement is incorrect : ( R= Radius of the earth)