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7.Gravitation
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The ratio of kinetic energy of a planet at perigee and apogee during its motion around the sun in elliptical orbit of eccentricity $e$ is ..........
A
$1: e$
B
$\frac{1+e}{1-e}$
C
$\left(\frac{1+e}{1-e}\right)^2$
D
$\left(\frac{1-e}{1+e}\right)^2$
Solution
(c)
$K.E$ of a planet $=\frac{1}{2} m v^2$
$K.E$ at perigee $=\frac{1}{2} m v_P^2$
$K.E$ at apogee $=\frac{1}{2} m v_A^2$
Using conservation of angular momentum at $P$ and $A$
$\Rightarrow m v_P r_P=m v_A r_A$
$\Rightarrow \frac{v_P}{v_A}=\frac{r_A}{r_P}=\frac{a(1+e)}{a(1-e)}$
$\Rightarrow \frac{ K \cdot E _P}{ K \cdot E _A}=\frac{v_P^2}{v_A^2}=\left(\frac{1+e}{1-e}\right)^2$
Standard 11
Physics
