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7.Gravitation
medium
If the density of the earth is doubled keeping its radius constant, then acceleration due to gravity will be ........ $m/s^2$. $(g = 9.8\,m/sec^2)$
A
$19.6$
B
$9.8$
C
$4.9$
D
$2.45$
Solution
$g=\left(G M / R^{2}\right)=\left(G / R^{2}\right) \times(4 / 3) \pi R^{3} \times \rho=(4 / 3) \pi G R \rho$
Radius is kept constant
$g \propto \rho$
$g_{2}=g_{1}\left(\rho_{2} / \rho_{1}\right)$
Density is doubled hence $\rho_{2}=2 \rho_{1}$
$g_{2}=g_{1} \times 2$
$\mathrm{g}_{2}=19.6 \mathrm{m} / \mathrm{s}^{2}$
Standard 11
Physics
