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7.Gravitation
easy
Two planets have same density but different radii. The acceleration due to gravity would be ........
A
Same on both planets
B
Greater on the smaller planet
C
Greater on the larger planet
D
Dependent on the distance of planet from the sun
Solution
(c)
Acceleration due to gravity at the surface of a planet, $g=\frac{G M}{R^2}$
where $M$ is the mass of planet,
$R$ is the radius of the planet,
Also, $M=p V$
$\Rightarrow g=\frac{G}{R^2} \times\left(\frac{4}{3} \pi G R^3 \rho\right)$
Thus, $g=\frac{4}{3} \pi G R \rho$
Thus $g \alpha$ Radius of the planet,
Thus, acceleration due to gravity would be greater on the larger planet.
Standard 11
Physics
