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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 `(g_1//g_2)` at their surfaces 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) 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

    A
    `(R_1rho_2)/(R_2rho_1)`
    B
    `(R_1rho_1)/(R_2rho_2)`
    C
    `(rho_1R_2^2)/(rho_2R_1^2)`
    D
    `(R_1R_2)/(rho_1rho_2)`

  • The density of the core a planet is rho_(1) and that of the outer shell is rho_(2) . The radii of the core and that of the planet are R and 2R respectively. The acceleration due to gravity at the surface of the planet is same as at a depth R . Find the ratio of (rho_(1))/(rho_(2))

    A
    2.3
    B
    4.5
    C
    3.2
    D
    5.4

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