A meter rule is found to balance horizontally at the 48cm mark. When a body of mass 80g is suspended at the 8cm mark, the balance point is found to be 30cm mark. Calculate the mass of the meter rule
Answers
To solve this problem, we can use the principle of moments. The principle of moments states that for an object to be in equilibrium, the sum of the clockwise moments must be equal to the sum of the anticlockwise moments.
First, let's find the moments created by the meter rule and the body:
Moment of the meter rule (M1) = mass of the meter rule (M) × distance from the balance point (48 cm)
Moment of the body (M2) = mass of the body (m) × distance from the balance point (8 cm)
Since the meter rule is balanced horizontally, the sum of the clockwise moments (M2) should be equal to the sum of the anticlockwise moments (M1).
M2 = M1
m × 8 cm = M × 48 cm
Now, we have another condition where the balance point is at the 30 cm mark when the body is suspended at the 8 cm mark. Using the same principle of moments:
M1 = m × 30 cm
Equating the two values of M1, we get:
M × 48 cm = m × 30 cm
Now, let's plug in the values we know. The mass of the body is given as 80 g (which can be converted to 0.08 kg by dividing by 1000 since 1 kg = 1000 g). The distance from the balance point is given as 8 cm.
0.08 kg × 8 cm = M × 48 cm
Now, let's solve for M:
0.64 kg·cm = 48 M cm
Dividing both sides by 48 cm:
0.01333 kg = M
Therefore, the mass of the meter rule is approximately 0.01333 kg or 13.33 grams.