JEE Mains · Physics · STD 11 - 7. gravitation
Figure shows elliptical path \(abcd\) of a planet around the sun \(S\) such that the area of triangle \(csa\) is \(\frac {1}{4}\) the area of the ellipse. (See figure) With \(db\) as the semimajor axis, and \(ca\) as the semiminor axis. If \(t_1\) is the time taken for planet to go over path \(abc\) and \(t_2\) for path taken over \(cda\) then
- A \(t_1 = 4t_2\)
- B \(t_1 = 2t_2\)
- C \(t_1 = 3t_2\)
- D \(t_1 = t_2\)
Answer & Solution
Correct Answer
(C) \(t_1 = 3t_2\)
Step-by-step Solution
Detailed explanation
Let area of ellipse abcd \(=x\) Area of \(SabcS\) \( = \frac{x}{2} + \frac{x}{4}\,\left( {i.e.,\,ar\,of\,abcd + SacS} \right)\) \(\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(Area\,of\,half\,ellipse + Area\,of\,triangle)\) \( = \frac{{3x}}{4}\)…
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