Gravitation

JEE Main level, single correct, medium

56 of 223

Question 56 of 223

Two planets A and B of radii RR and 1.5R1.5R have densities ρ\rho and ρ2\dfrac{\rho }{2} respectively. The ratio of acceleration due to gravity at the surface of B to A is:

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Answer: (C) 3:43:4

The acceleration due to gravity is
g=GMR2=4πGRρ3⇒g∝ρ⋅Rg=\dfrac{GM}{{R}^{2}}=\dfrac{4\pi GR\rho }{3} \Rightarrow g\propto \rho \cdot R
Thus, the ratio is
⇒gBgA=1.5Rρ2ρR=12×1.5=0.75⇒gBgA=34\Rightarrow \dfrac{{g}_{B}}{{g}_{A}}=\dfrac{1.5R\rho }{2\rho R}=\dfrac{1}{2}\times 1.5=0.75 \Rightarrow \dfrac{{g}_{B}}{{g}_{A}}=\dfrac{3}{4}

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