Consider two planets with equal masses having radius $r_{1}$ and $r_{2}$ such that $r_{1} > r_{2}$ . The force of gravities at their surfaces are $F_{1}$ and $F_{2}$ respectively for a mass $m$ . Which of the following conditions are true?

F_{1} > F_{2}

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F_{1} < F_{2}

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F_{1} = F_{2}

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F_{1} \leq F_{2}

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Solution

The correct option is B $F_{1} < F_{2}$
Acceleration due to gravity is given by:
$g = \frac{G M}{R^{2}}$

It is given mass is same for both the planets.
$⟹ g \propto \frac{1}{R^{2}}$

Since $r_{1} > r_{2}$ ,
$g_{1} < g_{2}$

From Newton's second law, force is proportional to acceleration.
$∴ F_{1} > F_{2}$

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Consider two planets with equal masses having radius r1 and r2 such that r1>r2. The force of gravities at their surfaces are F1 and F2 respectively for a mass m. Which of the following conditions are true?

The correct option is B F1<F2Acceleration due to gravity is given by: g=GMR2 It is given mass is same for both the planets. ⟹g∝1R2 Since r1>r2, g1<g2 From Newton's second law, force is proportional to acceleration. ∴F1>F2

Consider two planets with equal masses having radius $r_{1}$ and $r_{2}$ such that $r_{1} > r_{2}$ . The force of gravities at their surfaces are $F_{1}$ and $F_{2}$ respectively for a mass $m$ . Which of the following conditions are true?