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  4. Figure shows elliptical path abcd of a planet around the sun S such that the area of triangle csa is (1/4) 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 :

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Q. 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 :Physics Question Image

JEE MainJEE Main 2016Gravitation

Solution:

Area abca = x
Area SABCS $=x+\frac{1}{2}x$
Area SADCS $=x-\frac{1}{2}x=\frac{1}{2}$
$\frac{1+\frac{1}{2}}{1-\frac{1}{2}}=\frac{t_{1}}{t_{2}}$
$\frac{\frac{3}{2}}{\frac{1}{2}}=\frac{t_{1}}{t_{2}}\,t_{1}=3t_{2}$
$\frac{3}{1}=\frac{t_{1}}{t_{2}}$

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