A satellite is rotating around a planet in the orbi of radius r with time period T. If gravitational force changes according to $r^{5 / 2}$ the $T^{2}$ will be

\propto r^{3}

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\propto r^{7 / 2}

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\propto r^{9 / 2}

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\propto r^{3 / 2}

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Solution

The correct option is B $\propto r^{7 / 2}$
$\frac{G M m}{r^{5 / 2}} = \frac{m v^{2}}{r}$
$v^{2} = \frac{G M}{r^{3 / 2}}$
$T^{2} = {(\frac{2 π r}{v})}^{2}$
$= \frac{4 π^{2} r^{2}}{G M / r^{3 / 2}} = \frac{4 π^{2} r^{7 / 2}}{G m}$
$T^{2} \propto r^{7 / 2}$

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A satellite is rotating around a planet in the orbi of radius r with time period T. If gravitational force changes according to r5/2 the T2 will be

The correct option is B ∝r7/2GMmr5/2=mv2rv2=GMr3/2T2=(2πrv)2=4π2r2GM/r3/2=4π2r7/2GmT2∝r7/2

A satellite is rotating around a planet in the orbi of radius r with time period T. If gravitational force changes according to $r^{5 / 2}$ the $T^{2}$ will be

The correct option is B $\propto r^{7 / 2}$
$\frac{G M m}{r^{5 / 2}} = \frac{m v^{2}}{r}$
$v^{2} = \frac{G M}{r^{3 / 2}}$
$T^{2} = {(\frac{2 π r}{v})}^{2}$
$= \frac{4 π^{2} r^{2}}{G M / r^{3 / 2}} = \frac{4 π^{2} r^{7 / 2}}{G m}$
$T^{2} \propto r^{7 / 2}$