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?

The mass of the unknown body is 4.00 kg

Explanation:

To solve the problems within the masses we must set a reference system, we will place it in the unknown mass. The equation for the center of masses

Xcm = ∑ Xi mi / Mt

With xi the distance from the reference system, mi body mass and Mt all masses.

In our case

m1 0 1.00 kg

Xi = 2.00 m

The unknown body is on the reference system

m2 = ?

X2 = 0 m

We calculate the position of the mass center for our reference system

Xcm = 2 - 1.6

Xcm = 0.400 m

We substitute and calculate

Xcm = m1 X1 / (1 + m2)

(1 + m2) = m1 X1 / Xcm

(1 + m2) = 1.00 2.00 / 0.4.00

(1 + m2) = 5.00

m2 = 5.00 - 1

m2 = 4.00 Kg

The mass of the unknown body is 4.00 kg