# The radii of the earth and the moon are in the ratio 10 : 1 while acceleration due to gravity on the earth’s surface and moon’s surface are in the ratio 6 : 1. The ratio of escape velocities from earth’s surface to that of moon surface is Option 1) $10 : 1$ Option 2) 6 : 1 Option 3) 1.66 : 1 Option 4) 7.74 : 1

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

Escape velocity = $\sqrt{\frac{2GM}{R}}=\sqrt{2gR}$

$\frac{V_{1}}{V_{2}}=\sqrt{\frac{g_{1}}{g_{2}}.\frac{R_{1}}{R_{2}}}$

$=\sqrt{\frac{10}{1}.\frac{6}{1}}=\sqrt{60}:1=7.74:1$

Option 1)

$10 : 1$

This is incorrect option

Option 2)

6 : 1

This is incorrect option

Option 3)

1.66 : 1

This is incorrect option

Option 4)

7.74 : 1

This is correct option

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