A 14 kilogram beam is hinged at one end. A 6.0-kilogram triangular object and a 7.5-kilogram capital I-shaped object are placed as shown in the figure. The dots indicate the individual centers of gravity of the beam and objects. The center of mass of the entire system must be:

1.3 m

Explanation:

From the figure attached, 3 materials are involved. A 14 kilogram beam hinged at one end, a 6.0-kilogram triangular object and a 7.5-kilogram capital I-shaped object.

Let take the moment at the hinge axis.

The moment for the beam will be

14 × ( 0.36 + 0.53 ) = 12.6

The moment of the triangle object will be 6 × 0.36 = 2.16

The moment of capital I shape will be

7.5 × ( 0.36 + 0.53 + 1.92 ) = 21.075

The total moment = 12.6 + 2.16 + 21.075

The total moment = 35.835

The total mass = 14 + 6 + 7.5 = 27.5

The center of mass of the entire system must be:

X = total moment ÷ total mass

Substitute both in the formula

X = 35.835/27.5

X = 1.3 m.

Therefore, The center of mass of the entire system must be 1.3m

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