Is it true that for a object moving in circular orbit if the radius of the orbit increases then the velocity of the object moving in the circular orbit also increases?

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No, that is not true.  The velocity actually decreases with increasing radius.  This works kind of like a balancing act, the length of the radius versus the velocity the object.  You can demonstrate this radius versus velocity yourself, if you get a length of string and tie a weighted object on the end of it.  Whirl the object around your hand in a circular orbit, then allow the string to wind on your fingers.  Observe what happens to the velocity of the object as the string gets shorter.  It gets progressively faster the shorter the string becomes.  So the shorter the radius the faster the velocity.  This must occur because the pull of gravity becomes stronger as you decrease the distance between the objects.  This effect may also be observed with increasing distance of the planets away from the sun.  The farther out the planet is, the longer it takes to go around the sun.  This is partly due to the increased distance, while also due to decreased velocity.

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