A meter stick balances at the 50.0-cm mark.If a mass of 50.0 g is placed at the 90.0-cm mark,the stick balances at the 61.3-cm mark.What is the mass of the meter stick?
A)127 g
B)178 g
C)89.7 g
D)32.6 g
E)73.4 g

Question

Quizplus · Accepted Answer

The meter stick initially balances at the 50.0-cm mark, indicating that its center of mass is at the 50.0-cm mark. When a 50.0 g mass is placed at the 90.0-cm mark and the new balance point is at the 61.3 cm, we can use the principle of moments (torque) to find the mass of the meter stick. The moment caused by the meter stick's mass about the new balance point must equal the moment caused by the added mass. Let $M$ be the mass of the meter stick. The distance from the center of mass of the meter stick to the new balance point is $50.0 - 61.3 = -11.3$ cm (negative because it's to the left of the balance point), and the distance from the added mass to the balance point is $90.0 - 61.3 = 28.7$ cm. Setting the moments equal gives us:$$M \times (-11.3) = 50.0 \times 28.7$$Solving for $M$ gives:$$M = \frac{50.0 \times 28.7}{11.3} \approx 127 \, \text{g}$$Therefore, the mass of the meter stick is approximately 127 g.

A Meter Stick Balances at the 50