Question

A 1.90-m-long barbell has a 25.0 kg weight on its left end and a 37.0 kg weight on its right end. if you ignore the weight of the bar itself, how far from the left end of the barbell is the center of gravity?

Answer 1

Answer: The center of gravity is 1.1338 m away from the left side of the barbell

Explanation:

Length of the barbell = 1.90 m

The distance center of gravity from left = x

Mass on the left side = 25 kg

The distance center of gravity from right = 1.90 - x

Mass on the right side = 37 kg

At the balance point: $m_1x_1=m_2x_2$

$25 kg\times x=37 kg\times (1.90-x)$

$x=1.1338 m$

The center of gravity is 1.1338 m away from the left side of the barbell

Answer 2

To solve for the distance from the left end of the barbell:37 * 1.9 = ( 37 + 25) * x x = 37*1.9 / (37+20) = 1.23333 m 
Additional info: if we are going to repeat this with a uniform bar of mass 9kg whose center of mass is 0.75 m from the left, the answer would be
37 * 1.9 + 9 * 0.75 = (37 + 25+ 9) * y y = (37 *1.9 + 8 * 0.75) / (37 + 25 + 9) = 1.07 m