question_answer

The kinetic energies of a planet in an elliptical orbit about the Sun, at positions A, B and C are\[{{\text{K}}_{\text{A}}}\], \[{{\text{K}}_{\text{B}}}\] and\[{{\text{K}}_{\text{C}}}\], respectively. AC is the major axis and SB is perpendicular to AC at the position of the Sun S as shown in the figure. Then                         [NEET - 2018]

A)  \[{{\text{K}}_{\text{B}}}\text{}{{\text{K}}_{\text{A}}}\text{}{{\text{K}}_{\text{C}}}\]         

B)  \[{{\text{K}}_{\text{A}}}\text{}{{\text{K}}_{\text{B}}}\text{}{{\text{K}}_{\text{C}}}\]

C)  \[{{\text{K}}_{\text{A}}}\text{}{{\text{K}}_{\text{B}}}\text{}{{\text{K}}_{\text{C}}}\]         

D)  \[{{\text{K}}_{\text{B}}}\text{}{{\text{K}}_{\text{A}}}\text{}{{\text{K}}_{\text{C}}}\]

Correct Answer: B

Solution :

Point A is perihelion and C is aphelion. So, \[{{\text{V}}_{\text{A}}}\text{}{{\text{V}}_{\text{B}}}\text{}{{\text{V}}_{\text{C}}}\] So, \[{{\text{K}}_{\text{A}}}\text{}{{\text{K}}_{\text{B}}}\text{}{{\text{K}}_{\text{C}}}\]