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Consider Earth to be stationary, and the moon as orbiting Earth in a circle of radius R. If the masses of Earth and the Moon are ME and Mm, respectively, which of the following best represents the total mechanical energy of the Earth-Moon system?a. [tex]\frac{GM_EM_M}{2R}[/tex]
b. [tex]\frac{GM_EM_M}{R}[/tex]
c. [tex]-\frac{GM_EM_M}{2R}[/tex]
d. [tex]-\frac{GM_EM_M}{R}[/tex]
e. [tex]-\frac{2GM_EM_M}{R}[/tex]

Respuesta :

Answer:

option C

Explanation:

given,

mass of earth = Me

mass of the moon = Mm

radius = R

Total mechanical energy = ?

Kinetic energy of moon =

[tex]KE = \dfrac{1}{2}M_m v^2[/tex]

velocity of the moon is equal to

[tex]v = \sqrt{\dfrac{GM_e}{R}}[/tex]

total energy =[tex]-\dfrac{1}{2}M_m v^2[/tex]

now, putting value of in the above equation

[tex]TE = -\dfrac{1}{2}M_m (\sqrt{\dfrac{GM_e}{R}})^2[/tex]

[tex]TE = -\dfrac{1}{2}M_m\dfrac{GM_e}{R}[/tex]

[tex]TE = -\dfrac{1}{2}\dfrac{GM_mM_e}{R}[/tex]

[tex]TE = -\dfrac{GM_mM_e}{2R}[/tex]

hence, the correct answer is option C

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