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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}

 
Answers (1)
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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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