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The radii of two planets are respectivel...

The radii of two planets are respectively `R_(1) and R_(2)` and their densities are respectively `rho_(1) and rho_(2)`.The ratio of the accelerations due to gravity at their surface is

Text Solution

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As `g=(GM)/(R^(2))=G/(R^(2))xx4/3piR^(3)rho=4/3piGRrho`,so `gpropRrho`
`:. (g_(1))/(g_(2))=(R_(1)rho_(1))/(r_(2)rho_(2))`
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Knowledge Check

  • The radii of two planets are respectively R_(1) & R_(2) and their densities are respectively rho_(1) and rho_(2) . The ratio of the acceleration due to gravity at their surface is

    A
    `g_(1):g_(2)=(rho_(1))/(R_(1)^(2)):(rho_(2))/(R_(2)^(2))`
    B
    `g_(1):g_(2)=R_(1)R_(2)=rho_(1)rho_(2)`
    C
    `g_(1):g_(2)=R_(1)rho_(2):R_(2)rho_(1)`
    D
    `g_(1):g_(2)=R_(1)rho_(1):R_(2)rho_(2)`

  • R and r are the radii of the earth and moon respectively. rho_(e) and rho_(m) are the densities of earth and moon respectively. The ratio of the accelerations due to gravity on the surfaces of earth and moon is

    A
    `R/r rho_(e)/rho_(m)`
    B
    `r/R rho_(e)/rho_(m)`
    C
    `r/R rho_(m)/rho_(e)`
    D
    `R/r rho_(e)/rho_(m)`

  • Two planets have radii r_(1) and 2r_(1) and densities are rho_(1) and 4rho_(1) respectively. The ratio of their acceleration due to gravities is

    A
    `1:8`
    B
    `8:1`
    C
    `4:1`
    D
    `1:4`

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