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7.Gravitation
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Imagine a new planet having the same density as that of earth but it is $3$ times bigger than the earth in size. If the acceleration due to gravity on the surface of earth is $g$ and that on the surface of the new planet is $g^{\prime}$, then
A
$g^{\prime}=g/9$
B
$g^{\prime}=27 g$
C
$g^{\prime}=9 g$
D
$g^{\prime}=3 g$
(AIPMT-2005)
Solution
$g=\frac{G M}{r^{2}}=\frac{G}{r^{2}}\left(\frac{4}{3} \times r^{3} \rho\right)=\frac{4}{3} \times \rho G r$
$\frac{g^{\prime}}{g}=\frac{3 R}{R} \Rightarrow g^{\prime}=3 g$
Standard 11
Physics
