Question

A mere rule is found to be balance horizontally at the 48cm mark, when a body of mass 60g is suspended at the 6cm mark, the balance point is found to be at the 30cm mark.

Calculate the mass of the metre rule

Answer 1

60 g * (30 cm - 6 cm) = m (48 cm - 30 cm)

Answer 2

I need the the solution of the question

Answer 3

[AI-generated answer — Explain Bot]

To calculate the mass of the meter rule, we need to use the principle of moments. The principle of moments states that the sum of the moments of a system in equilibrium is zero.

First, let's denote the mass of the meter rule as M, the distance from the pivot to the suspended body as d1 (6cm in this case), and the distance from the pivot to the center of gravity of the meter rule as d2 (which we need to find).

For the rule to be balanced horizontally at the 48cm mark, the clockwise moment created by the rule (M) must be equal to the anticlockwise moment created by the suspended body (mass = 60g, distance = 6cm).
Thus, M * d2 = 60g * 6cm

For the balance point to be at the 30cm mark, the clockwise moment created by the rule must be equal to the anticlockwise moment created by the suspended body plus the clockwise moment created by the suspended body.
Thus, M * (d2 - 30cm) = 60g * 6cm + 60g * (30cm - 6cm)

Now, we can solve these equations simultaneously to find the value of M.

Step 1: Rewrite the equation from the first condition:
M * d2 = 60g * 6cm (Eq.1)

Step 2: Expand and rewrite the equation from the second condition:
M * (d2 - 30cm) = 60g * 6cm + 60g * (30cm - 6cm)
M * d2 - 30cm * M = 60g * 6cm + 60g * 24cm
M * d2 - 30cm * M = 60g * (6cm + 24cm)
M * d2 - 30cm * M = 60g * 30cm
M * d2 = 60g * 30cm + 30cm * M (Eq.2)

Step 3: Substitute Eq.1 into Eq.2 and solve for M:
60g * 6cm = 60g * 30cm + 30cm * M
360g*cm = 1800g*cm + 30cm * M
30cm * M = 1440g*cm
M = 1440g*cm / 30cm
M = 48g

Therefore, the mass of the meter rule is 48 grams.