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The moon's radius is 1//4 that of the e...

The moon's radius is `1//4` that of the earth and its mass is `1//80` times that of the earth. If g represents the
acceleration due to gravity on the surface of the earth, that on the surface of the moon is

A

`(g)/(4)`

B

`(g)/(5)`

C

`(g)/(6)`

D

`(g)/(8)`

Text Solution

Verified by Experts

The correct Answer is:
B
Acceleration due to gravity g = `("GM")/(R^(2))`
`therefore (g_("moon"))/(g_("earth"))=(M_("moon"))/(M_("earth")).(R_("earth")^(2))/(R_("moon"^(2)))=(1/(80))(4/1)^(2)`
`g_("moon")=g_("earth") xx (16)/(80)=(g)/(5)`
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Knowledge Check

  • The acceleration of a body due to the attraction of hte earth (radius R) at a distace 2R from the surface of the earth is (g = acceleration due to gravity at the surface of the earth )

    A
    `(g)/(9)`
    B
    `(g)/(3)`
    C
    `(g)/(4)`
    D
    g

  • The acceleration of a body due to the attraction of the earth (radius R) at a distance 2R from the surface of the earth is (g=acceleration due to gravity at the surface of the earth)

    A
    `(g)/(9)`
    B
    `(g)/(3)`
    C
    `(g)/(4)`
    D
    g

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    A
    R
    B
    `(3R)/(4)`
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    `(R)/(2)`
    D
    `(R)/(4)`

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