A 2.00-m rod of negligible mass connects two very small objects at its ends.The mass of one object is 1.00 kg and the mass of the other is unknown.The center of mass of this system is on the rod a distance 1.60 m from the 1.00-kg mass object.What is the mass of the other object?

Question

Quizplus · Accepted Answer

Let the mass of the unknown object be m.

From the given information, we know that:

1) The total length of the rod is 2.00 m. 
2) The center of mass of the system is 1.60 m from the 1.00 kg mass object.

We can use the equation for the center of mass of a two-object system:

x_cm = (m1*x1 + m2*x2) / (m1 + m2)

where

x1 = distance from the 1.00 kg mass object to the center of mass 
x2 = distance from the unknown object to the center of mass

Substituting the given values, we get:

1.60 m = (1.00 kg * 0 m + m * (2.00 m - x2)) / (1.00 kg + m)

Solving for m, we get:

m = 4.00 kg

Therefore, the mass of the other object is 4.00 kg, which is answer choice C.

A 200-M Rod of Negligible Mass Connects Two Very Small Objects