A uniform half metre is freely pivoted at 15cm mark and it balances horizontally when a body of mass 40g is hung from a 2cm mark. Calculate the mass of the rule.
To find the mass of the rule, we can use the principle of moments based on the fact that the rule is balanced horizontally. The principle of moments states that the sum of the clockwise moments is equal to the sum of the anticlockwise moments.
Let's denote the mass of the rule as M, and the distance from the pivot to the 40g mass as x. In this case, x is the distance between the 15cm mark and the center of mass of the rule.
Based on the information given, we have:
Mass of the body hanging from the 2cm mark (40g) × Distance from pivot to body (x) = Mass of the rule (M) × Distance from pivot to center of mass of the rule (15cm)
Converting the given measurements to meters:
40g = 0.04kg
2cm = 0.02m
15cm = 0.15m
Plugging in the values we have:
0.04kg × 0.02m = M × 0.15m
Simplifying the equation:
0.0008kg·m = 0.15M
Now, to find the mass of the rule (M), we can isolate it in the equation:
M = 0.0008kg·m / 0.15m
Simplifying further:
M = 0.00533kg
Therefore, the mass of the rule is approximately 0.00533kg.