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

 

Answers (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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