10. Two satellites orbit the Earth in circular orbits of the same radius.One satellite is twice as massive as the other. Which statement is true about the speeds of these satellites? (a) The heavier satellite moves twice as fast as the lighter one. (b) The two satellites have the same speed. (c) The lighter satellite moves twice as fast as the heavier one. (d) The ratio of their speeds depends on the orbital radius.

The correct answer is (b) The two satellites have the same speed.<br /><br />Explanation:<br /><br />The speed of a satellite in a circular orbit around the Earth is given by the equation:<br /><br />v = √(GM/r)<br /><br />where:<br />- v is the orbital speed of the satellite<br />- G is the gravitational constant<br />- M is the mass of the Earth<br />- r is the radius of the orbit<br /><br />Since the two satellites have the same orbital radius, the only difference between their speeds is the mass of the Earth, which is the same for both satellites. Therefore, the two satellites have the same speed, regardless of their individual masses.<br /><br />The other options are incorrect:<br />(a) The heavier satellite does not move twice as fast as the lighter one, since the speed depends only on the Earth's mass and the orbital radius, not the satellite's mass.<br />(c) The lighter satellite does not move twice as fast as the heavier one, for the same reason as (a).<br />(d) The ratio of their speeds does not depend on the orbital radius, since the radius is the same for both satellites.