Q

Give answer! Two planets of radii r1 and r2 are made from the same material. The ratio of the acceleration due to gravity g1/g2 at the surface of the two planets is

Two planets of radii r1 and r2 are made from the same material. The ratio of the acceleration due to gravity g1/g2 at the surface of the two planets is

• Option 1)

$\frac{r1}{r2}$

• Option 2)

$\frac{r2}{r1}$

• Option 3)

$\left ( \frac{r1}{r2} \right )^{2}$

• Option 4)

$\left ( \frac{r2}{r1} \right )^{2}$

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As we learnt in

Acceleration due to gravity (g) -

Force extended by earth on a body is gravity.

Formula:    $g=\frac{GM}{R^{2}},$

$g=\frac{4}{3}\pi \rho \, GR$

$g\rightarrow$ gravity

$\rho \rightarrow$ density of earth

$R \rightarrow$ Radius of earth

- wherein

It's average value is $9.8\: m/s^{2}\; \; or \; \; 981cm/sec^{2}\; or\; 32feet/s^{2}$ on the surface of earth

Since both are made of same material hence their densities are equal

$g=\frac{GM}{R^{2}}=\frac{G.\rho .\frac{4\pi}{3}R^{3}}{R^{2}}$

$g=\frac{4\pi \rho GR}{3}\ \: \: \Rightarrow \frac{g_{1}}{g_{2}}=\frac{r_{1}}{r_{2}}$

Option 1)

$\frac{r1}{r2}$

This is correct option

Option 2)

$\frac{r2}{r1}$

This is incorrect option

Option 3)

$\left ( \frac{r1}{r2} \right )^{2}$

This is incorrect option

Option 4)

$\left ( \frac{r2}{r1} \right )^{2}$

This is incorrect option

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