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The radius of the Moon is about one-four...

The radius of the Moon is about one-fourth that of the Earth and acceleration due to gravity on the Moon is about one-sixth that on the Earth From this, we can conclude that the ratio of mass of Earth to the mass of the Moon is about

A

10

B

100

C

1000

D

10000

Text Solution

Verified by Experts

The correct Answer is:
B
`R_m=R_e//4 , g_m=g_e//6`
`g=GM//R_2`
`g_e//g_m=(M_e//R_e^2)//(M_m//R_m)^2`
`g_e//g_m=(M_e//M_m)//(R_m//R_e)^2`
`(M_e//M_m)=(g_e//g_m)X(R_e//R_m)^2=(6g_m//g_m)X (4R_m//R_m)^2`
`=6xx4xx4=96~~100`
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Knowledge Check

  • If acceleration due to gravity on the moon is one-sixth that on the earth, then the length and time period of seconds pendulum on the surface of moon are

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    B
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    C
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    `1:80`
    B
    `80:1`
    C
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    D
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  • Assertion: The acceleration due to gravity on the moon is one-sixth that on the earth. Reason : The law of gravitation is the same on both the moon and the earth.

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