Then velocity in circular orbits is given as -xGM-r- Find x-

For a rotating body, centrifugal force = centripetal forceHere, centripetal force = GMmr^2 andcentrifugal force nbsp; =mv^2r So, nbsp; ...

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Standard XII

Physics

Satellites

then velocity...

Question

then velocity in circular orbits is given as $\sqrt{\frac{x G M}{r}}$ . Find $x$ .

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Solution

For a rotating body, centrifugal force $=$ centripetal force
Here, centripetal force $= \frac{G M m}{r^{2}}$ and
centrifugal force $= \frac{m v^{2}}{r}$
So, $\frac{G M m}{r^{2}} = \frac{m v^{2}}{r}$
On further simplification we get, $v = \sqrt{\frac{G M}{r}}$ . Thus, $x = 1$ .

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then velocity in circular orbits is given as √xGMr. Find x.

For a rotating body, centrifugal force = centripetal forceHere, centripetal force =GMmr2 andcentrifugal force =mv2rSo, GMmr2=mv2rOn further simplification we get, v=√GMr. Thus, x=1.

then velocity in circular orbits is given as $\sqrt{\frac{x G M}{r}}$ . Find $x$ .

For a rotating body, centrifugal force $=$ centripetal force
Here, centripetal force $= \frac{G M m}{r^{2}}$ and
centrifugal force $= \frac{m v^{2}}{r}$
So, $\frac{G M m}{r^{2}} = \frac{m v^{2}}{r}$
On further simplification we get, $v = \sqrt{\frac{G M}{r}}$ . Thus, $x = 1$ .