Is the Calculation for the Center of Gravity of Two Spheres and a Rod Correct?

[brotherbobby]

Homework Statement

A cylindrical rod has a mass of 10 kg and a length of 2 m. At either end of the rod are fitted a sphere each - the one on the left has a mass of 50 kg and a diameter of 0.2 m while that on the right has a mass of 20 kg and a diameter of 0.1 m. Calculate the c.g. of the combination

Answer (in textbook) $\boxed{\color {red} {x_C = 73 \;\text{cm}}}\; \text{from the center of the larger sphere}$

Relevant Equations

Center of gravity in one dimension : $x_C = \frac{\Sigma_i m_i x_i}{\Sigma m_i}$

I begin by drawing the problem. Let the center of the bigger sphere on the left by the origin for the system.

Calculating $x_C = \frac{10 \times 1.1 + 20 \times 2.15}{50+20+10} = \frac{54}{80} = 0.675\; \text{m} \;= \boxed{67.5 \; \text{cm}}\;$.

Problem is, doesn't match the answer in the text (given above).

Is my calculation alright?

 

[gleem]

Yes

 

[brotherbobby]

Yes

Thank you. Fortunately I am in contact with the author of the book, who needs to be written to.