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  • I have a doubt, kindly clarify. A particle of mass 'm' is kept at rest at a height 3 R from the surface of earth, where 'R' is radius of earth and 'M' is mass of earth. The minimum speed with which it should be projected, so t

A particle of mass 'm' is kept at rest at a height 3 R from the surface of earth, where 'R' is radius of earth and 'M' is mass of earth. The minimum speed with which it should be projected, so that it does not return back, is (g is acceleration due to gravity on the surface of the earth)

  • Option 1)

    \left ( \frac{GM}{R} \right )^\frac{1}{2}

  • Option 2)

    \left ( \frac{GM}{2R} \right )^\frac{1}{2}

  • Option 3)

    \left ( \frac{gR}{4} \right )^\frac{1}{2}

  • Option 4)

    \left ( \frac{2g}{4} \right )^\frac{1}{2}

 

Answers (1)

best_answer

As we learnt in

Escape velocity ( in terms of radius of planet) -

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

V_{c}=sqrt{2gR}

V_{c} ightarrow Escape velocity

R ightarrowRadius of earth

- wherein

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

 

 V_{e}=\sqrt{\frac{2Gm}{R}}=\sqrt{\frac{2Gm}{R+h}}=\sqrt{\frac{2Gm}{4R}}\left [ h=3R \right ]

V_{e}=\left ( \frac{Gm}{2R} \right )^{\frac{1}{2}}


Option 1)

\left ( \frac{GM}{R} \right )^\frac{1}{2}

Incorrect Option

Option 2)

\left ( \frac{GM}{2R} \right )^\frac{1}{2}

Correct Option

Option 3)

\left ( \frac{gR}{4} \right )^\frac{1}{2}

Incorrect Option

Option 4)

\left ( \frac{2g}{4} \right )^\frac{1}{2}

Incorrect Option

Posted by

Aadil

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