Find the speed of a particle in a circular orbit with radius 10²¹m around an object of mass 10¹⁸kg. (G = 6.67 *10^-11m/kg·s²) A) 1.50 * 10¹³m/s B) 6.67*10^-¹⁴m/s C) 3.87 * 10⁶m/s D) 2.58 * 10^-⁷m/s E) 4.91 *10^-⁷m/s

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Quizplus · Accepted Answer

The formula for the speed of a particle in circular orbit is $v=\sqrt{\frac{GM}{r}}$, where $G$ is the gravitational constant, $M$ is the mass of the object being orbited, and $r$ is the radius of the orbit. Plugging in the given values, we get $v=\sqrt{\frac{(6.67	imes10^{-11})(10^{18})}{10}}=\sqrt{(6.67	imes10^7)}\approx2.58	imes10^4=2.58	imes10^{-17}$ m/s. Therefore, the best choice is D.

Find the Speed of a Particle in a Circular Orbit