Question

Two planets are spiralling around the sun in circular orbits of ratio m,,:n and density ratio p,:q, the acceleration due to gravity g is the ratio of,__​

Answer 1

Explanation:

The answer is mp:nq

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Answer 2

Given,

The ratio of radius, R$_{1}$:R$_{2}$ = m:n

The ratio of density, d$_{1}$:d$_{2}$= p:q

To Find,

The ratio of the acceleration due to gravity (g).

Solution,

For sphere, volume= $\frac{4}{3} \pi R^{3}$

mass = density x volume

$\frac{M_{1} }{M_{2} } = \frac{d_{1}X\frac{4}{3} \pi R_{1} ^{3} }{d_{2} X \frac{4}{3} \pi R_{2} ^{3}}$ = $\frac{d_{1} X R_{1} }{d_{2} X R_{2} }$

$\frac{G_{1} }{g_{1} } =$ $\frac{GM_{1} }{R_{1} ^{2} }$ x $\frac{R_{2} ^{2} }{GM_{2} } =$ $\frac{M_{1} }{M_{2} } X \frac{R_{2} ^{2} }{R_{1} ^{2} }$= $\frac{d_{1}R_{1} }{d_{2}R_{2} }$ = $\frac{mp}{nq}$

∴ Hence, the ratio of acceleration due to gravity of the two planets is mp:nq