If escape velocity from the earth’s surface is 11.2 km/sec. then escape velocity from a planet of mass same as that of earth but radius one fourth as that of earth is

  • Option 1)

    11.2 km/sec

  • Option 2)

    22.4 km/sec

  • Option 3)

    5.65 km/sec

  • Option 4)

    44.8 km/sec

 

Answers (1)

As we learnt in 

Escape velocity ( in terms of radius of planet) -

V_{c}=\sqrt{\frac{2GM}{R}}

V_{c}=\sqrt{2gR}

V_{c}\rightarrow Escape velocity

R\rightarrowRadius of earth

- wherein

  • depends on the reference body
  • greater the value of \frac{M}{R} or \left ( gR \right ) greater will be the escape velocity V_{e}=11.2Km/s  For earth

 

 

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

\frac{V_{p}}{V_{e}}=\sqrt{\frac{R_{e}}{R_{p}}}=2

 \therefore V_{p}= 22.4 km/sec


Option 1)

11.2 km/sec

This is incorrect option

Option 2)

22.4 km/sec

This is correct option

Option 3)

5.65 km/sec

This is incorrect option

Option 4)

44.8 km/sec

This is incorrect option

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