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In: Physics

A 6.00-kg point mass and a 15.0-kg point mass are held in place 1.00 m apart....

A 6.00-kg point mass and a 15.0-kg point mass are held in place 1.00 m apart. A point particle of mass m = 1.00 kg is released from a point between the two masses such that the net gravitational force on this particle is zero. Call the line connecting all the masses x-axis.
a. Find the center of mass of this system.
b. Find the exact position of this point mass.
c. Calculate potential energy of this system.
d. If the 6.00-kg mass is then removed and m is allowed to orbit the 15.0-kg mass, calculate (i) the gravitational acceleration due to the 15.0-kg mass at the location of m, (ii) the centripetal acceleration of m (hint: how does the centripetal acceleration relate to the gravitational acceleration?), (iii) the period of its revolution around the 15.0-kg mass, assuming that it stays at the same distance away from the 15.0-kg mass, and (iv) the orbital speed of m around the 15.0-kg mass.

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