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QJEEM16Ph9ec3: JEE Main 2016 Physics - Class 11 JEEM16Ph9ec3 Solution: Figure shows elliptical path abcd of a planet around the sun S…

Figure shows elliptical path abcd of a planet around the sun S such that the area of triangle csa is 14{1 \over 4} the area of the ellipse. (See figure) With db as the semimajor axis, and ca as the semiminor axis. If t1 is the time taken for planet to go over path abc and t2 for path taken over cda then :

JEE Main 2016 (Online) 9th April Morning Slot Physics - Gravitation Question 163 English

Multiple Choice Options

  • A t1 = t2
  • B t1 = 2t2
  • C t1 = 3t2
  • D t1 = 4t2

Step-by-Step Verified Solution

Let the area of ellipse = A

∴\therefore    Area of abcSa = A2+A4{A \over 2} + {A \over 4} = Area of half of the ellipse + Area of the triangle = 3A4{{3A} \over 4}

Area of adcSa = A2−A4{A \over 2} - {A \over 4} = A4{A \over 4}

∴\therefore     t1t2{{{t_1}} \over {{t_2}}} = 3A4A4{{{{3A} \over 4}} \over {{A \over 4}}} = 3

∴\therefore    t1 = 3t2

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