question_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) [JEE Main Online Paper (Held On 11 April 2015)]  

A)  

B)  

C)  

D)  

Correct Answer: B

Solution :

  Potential V(r) due to large planet of radius R is given by \[\underset{out}{\mathop{V\left( r \right)}}\,=-\frac{GM}{r}\] \[r>R\] \[{{V}_{s}}\left( r \right)=\frac{-GM}{R}\] \[r=R\] \[{{V}_{in}}=-\frac{3}{2}\frac{GM}{R}\left[ 1-\frac{{{r}^{2}}}{3{{R}^{2}}} \right]\] \[r<R\]