An unknown mass is suspended by a string from

one end of an uniform stick which has a mass of
120 g. In order to balance the stick, it must be
supported one third of its length away from the mass. the unknown mass is therefore?

Let m be the unknown mass and M be the stick's mass. Stick length = L . The center of mass is L/6 from the fulcrum. The total moment about the fulcrum is zero.

m*g*(L/3) = M*g*(L/6)
m = M/2 = 60 g

To find the unknown mass, we need to set up an equation based on the given information. Let's assume that the length of the stick is L, and the unknown mass is M.

According to the problem, the stick needs to be supported one-third (1/3) of its length away from the mass. This means that the distance from the support point to the unknown mass is (1/3)*L.

To balance the stick, the torque on each side of the support point must be equal. Torque is a measure of rotational force and is calculated as the product of the force applied and the distance from the point of rotation.

On the side with the unknown mass, the torque is given by M*(1/3)*L, where M is the unknown mass.

On the side with the stick's mass (120g), the torque is given by (120g)*(L/3).

Since the stick is balanced, these two torques are equal:

M*(1/3)*L = (120g)*(L/3)

Now, we can cancel out the common factors and solve for M:

M = (120g)*(L/3) / (1/3)*L

Simplifying further:

M = 120g

Therefore, the unknown mass is 120 grams.