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  • Solve! A body of mass 'm' is taken from the earth's surface to the height equal to twice the radius (R) of the earth. The change in potential energy of body will be

A body of mass 'm' is taken from the earth's surface to the height equal to twice the radius (R) of the earth. The change in potential energy of body will be

  • Option 1)

    \frac{2}{3}mgR

  • Option 2)

    3 mgR

  • Option 3)

    \frac{1}{3}mgR

  • Option 4)

    mg2R

 

Answers (1)

best_answer

As we learnt in

Gravitational Potential Energy at centre of earth relative to infinity -

U=mleft ( -frac{3}{2}frac{GM}{R} ight )

m ightarrow mass of body

M ightarrow Mass of earth

- wherein

{Ucentre=mVcentre}\ {Vcentre ightarrow Potential: at: centre}

 

 U_{i}=\frac{-Gmm}{R}                                 \because R+2R=3R

U_{f}=\frac{-Gmm}{R}

\therefore change in potential energy

\Delta U=\frac{-Gmm}{3R}+\frac{Gmm}{R}=\frac{Gmm}{R}\left [ 1-\frac{1}{3} \right ]

\Delta U=\frac{2}{3}\frac{Gmm}{R}=\frac{2}{3}mgR


Option 1)

\frac{2}{3}mgR

Correct Option

Option 2)

3 mgR

Incorrect Option

Option 3)

\frac{1}{3}mgR

Incorrect Option

Option 4)

mg2R

Incorrect Option

Posted by

Plabita

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