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7.Gravitation
medium
Let kinetic energy of a satellite is $x$, then its time of revolution $T$ is proportional to ..............
A
$x^{-3}$
B
$x^{-3 / 2}$
C
$x^{-1}$
D
$\sqrt{x}$
Solution
(b)
Given that,
kinetic energy of satellite $=x$
To find, time of revolution $T \alpha$
$\because \frac{G m m}{2 r}=K \cdot E .$
Let $\frac{G m_m}{2}=c$
$\therefore \frac{c}{r}=k \cdot E \cdot x$.
Frum kepler's $3^{r d}$ law:
$T^2=r^3$
$T^2=\left(\frac{c}{x}\right)^3$
$T=\frac{c^{3 / 2}}{x^{3 / 2}}=c^{3 / 2} x^{-3 / 2}$
$\therefore T \propto x^{-3 / 2}\left(\because c^{3 / 2}=\right.$ constant $)$
Standard 11
Physics
