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7.Gravitation
medium
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 surfaces is
A
${g_1}:{g_2} = \frac{{{\rho _1}}}{{R_1^2}}:\frac{{{\rho _2}}}{{R_2^2}}$
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
${g_1}:{g_2} = {R_1}{\rho _1}:{R_2}{\rho _2}$
(AIIMS-2013)
Solution
(d) $g = \frac{4}{3}\pi \rho GR$
$\therefore \frac{{{g_1}}}{{{g_2}}} = \frac{{{R_1}{\rho _1}}}{{{R_2}{\rho _2}}}$
Standard 11
Physics
