If a body describes a circular motion under inverse square field, the time taken to complete one revolution $T$ is related to the radius of the circular orbit as
If a body describes a circular motion under inverse square field, the time taken to complete one revolution $T$ is related to the radius of the circular orbit as
$T \propto r$
$T \propto {r^2}$
${T^2} \propto {r^3}$
$T \propto {r^4}$
If a body describes a circular motion under inverse square field, the time taken to complete one revolution $T$ is related to the radius of the circular orbit as
$E \propto \frac{1}{r ^{2}}$
$F \propto \frac{1}{r^{2}}$
$F=\frac{k}{r ^{2}}$
$\frac{K}{r^{2}}=\frac{m v^{2}}{r}$ $T=\frac{2 \pi r}{v}$
$v^{2}=\frac{k}{m r}$
$v=\sqrt{\frac{k}{m r}}$
$T=\frac{2 \pi r}{\sqrt{\frac{R}{m r}}}$
$\Rightarrow T=\frac{2 \pi r^{3 / 2} m^{1 / 2}}{\sqrt{k}}$
$T^{2}=\frac{4 \pi^{2} r^{3} m}{ki}$
$T^{2} \propto r ^{3}$
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