Question

A meter stick is found to balance at the 49.7-cm mark when placed on a fulcrum. When a 50.0-gram mass is attached at the 10.0-cm mark, the fulcrum must be moved to the 39.2-cm mark for balance. What is the mass (in grams) of the meter stick?

Answer 1

Mass of the stick = 139.04 gram

Step-by-step explanation:

Let the mass of the meter stick be = M grams

given:

Attached mass, m = 50.0 gram

position of the fulcrum = 39.2 cm

The meter stick is balanced at 49.7 cm, therefore the center of mass of the stick will be at 49.7 cm

Now for the system to be balanced the moment due to all the masses about the fulcrum must be equal.

thus,

moment = Force × perpendicular distance from the point of movement

Force = mass × acceleration due to gravity(g)

therefore,

(refer figure for the distances)

50g × (39.2-10) = Mg × (49.7 - 39.2)

⇒
`M=(50* 29.2)/(10.5)`

⇒M = 139.04 gram