If an earth satellite of mass m orbiting at a distance 2 R from the centre of earth has to be transferred into the orbit of radius 3 R, the amount of energy required is (R = radius of earth)

Question

If an earth satellite of mass m orbiting at a distance 2 R from the centre of earth has to be transferred into the orbit of radius 3 R, the amount of energy required is (R = radius of earth) (A)  mgR  (B)  (mgR/3)  (C)  (mgR/2)  (D)  (mgR/12)

Tardigrade Admin · Accepted Answer

Energy require = Final energy - initial energy =-(GMm/2(3R))-[ (GMm/2(2R)) ] =(GMm/2(3R))-[ -(1/2)-(1/3) ] =(GMm/12R)=(gR2m/12R) =(mgR/12)

Q. If an earth satellite of mass $m$ orbiting at a distance $2 R$ from the centre of earth has to be transferred into the orbit of radius $3 R$ , the amount of energy required is (R = radius of earth)

$m g R$

$\frac{m g R}{3}$

$\frac{m g R}{2}$

$\frac{m g R}{12}$

$\frac{m g R}{9}$

Energy require = Final energy - initial energy
$= - \frac{GM m}{2 ( 3 R )} - [\frac{GM m}{2 ( 2 R )}]$
$= \frac{GM m}{2 ( 3 R )} - [- \frac{1}{2} - \frac{1}{3}]$
$= \frac{GM m}{12 R} = \frac{g R ^{2} m}{12 R}$
$= \frac{m g R}{12}$

Q. If an earth satellite of mass m orbiting at a distance 2R from the centre of earth has to be transferred into the orbit of radius 3R, the amount of energy required is (R = radius of earth)

mgR

3mgR​

2mgR​

12mgR​

9mgR​

Energy require = Final energy - initial energy =−2(3R)GMm​−[2(2R)GMm​] =2(3R)GMm​−[−21​−31​] =12RGMm​=12RgR2m​ =12mgR​