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  • Give answer! Which of the following most closely depicts the correct variation of the gravitation potential V(r) due to a large planet of radius R and uniform mass density ? (figures are not drawn to scale)

Which of the following most closely depicts the correct variation of the gravitation potential V(r) due to a large planet of radius R and uniform mass density ? (figures are not drawn to scale)

  • Option 1)

  • Option 2)

  • Option 3)

  • Option 4)

 

Answers (1)

best_answer

As we learnt in

Potential due to Uniform solid sphere -

R\rightarrow Radius of sphere

M\rightarrow Mass of sphere

r\rightarrow distance from centre of sphere

Vcentre=\frac{3}{2}Vsurface

- wherein

Outside the surface

V=-\frac{GM}{r}

on the surface

Vsurface=-\frac{GM}{R}

Inside the surface 

r<R

V=-\frac{GM}{2R}\left[3-\left ( \frac{r}{R} \right )^{2}\right]

 

 Potential v\left | r \right |  due to a large planet of radius R

v_0 (r) = -\frac{Gm}{r},\: r>R

v(r) = -\frac{Gm}{R},\: r=R

v_{in} = -\frac{3}{2}\frac{Gm}{R}[1-\frac{r^2}{3R^2}];\;\ r < R


Option 1)

Incorrect

Option 2)

Correct

Option 3)

Incorrect

Option 4)

Incorrect

Posted by

Plabita

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