A metre is found to balance at the 51cm mark . When a body of mass 70g is suspended at the 10cm mark the balance point is found to be at 250m mark find the mass of the ruler

Answer 1

Let m be the mass of the ruler, and let the original balance point at 51cm be the center of mass of the ruler.

At the original balance point, without the additional 70g mass:

Moment on the left side = Moment on the right side
m * (51 - 10) cm = m * (250 - 51) cm
m * 41 cm = m * 199 cm

When the 70g mass is added at the 10cm mark, the new balance point is at the 250 cm mark:

Moment on the left side + Moment due to 70g mass = Moment on the right side
m * (250 - 10) cm + 70g * (250 - 250) cm = m * (250 - 250) cm
m * 240 cm = 0

Because the total moment on each side is equal, the mass of the ruler doesn't matter in this problem. The key is to realize that the problem is not really asking for the mass of the ruler, but rather a relationship between the two balance points.

From the original balance point equation, we can solve for m/41:

m/41 = m/199

Simplifying this equation:

199 = 41

However, this equation does not make sense, as the balance points indicated in the problem cannot be correct. There must be an error in the problem statement, as the balance points provided would not lead to a mathematically possible scenario for the mass of the ruler.