The kinetic energy needed to project a body of  mass m from the earth surface (radius R) to infinity is

  • Option 1)

    m g R/2

  • Option 2)

    2m g R

  • Option 3)

    mgR

  • Option 4)

    m g R/4

 

Answers (1)
V Vakul

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

 

v_{e}=\sqrt{2gR}

 

\therefore Kinetic Energy = \frac{1}{2}mv_{e}^{2}\:=\:\frac{1}{2}m(2gR)\:=mgR

 


Option 1)

m g R/2

This option is incorrect.

Option 2)

2m g R

This option is incorrect.

Option 3)

mgR

This option is correct.

Option 4)

m g R/4

This option is incorrect.

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