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
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.
To solve this problem, we can use the concept of torques or moments.
Let's assume the mass of the ruler is "M" grams.
According to the problem, when a body of mass 70 grams is suspended at the 10cm mark, the balance point is at the 250cm mark.
We can set up an equation based on the principle of moments:
(M × distance from balance point to ruler's center of mass) = (mass of suspended body × distance from balance point to suspended body)
Using the distances given in centimeters:
(M × 51) = (70 × 240)
Now, let's solve for M:
M = (70 × 240) / 51
M ≈ 329.41 grams
Therefore, the mass of the ruler is approximately 329.41 grams.
To find the mass of the ruler, we can use the principle of lever balance.
Let's assume the mass of the ruler is represented by M.
Given information:
- The ruler balances at the 51cm mark when it is empty.
- When a body of mass 70g is suspended at the 10cm mark, the balance point is at the 250cm mark.
To find the mass of the ruler, we can set up an equation based on the principle of moments.
Moments on both sides of the balance point should be balanced:
(70g) × (10cm) = M × (250cm - 51cm)
Now, let's solve the equation:
(70g) × (10cm) = M × (250cm - 51cm)
700g cm = M × 199cm
700g cm / 199cm = M
M ≈ 3.5176 grams
Therefore, the mass of the ruler is approximately 3.5176 grams.