A uniform meter rule is balanced at 30cm mark when a mass of 50g is hanging from its zero mark. calculate the weight of the rule.
moments about zero point, m down at middle, m+50 up at 30
m * 50 cm = (m +50) * 30
(50-30) m = 1500
20 m = 1500
m = 75 grams
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Now, I do not know if you are in a physics class that uses SCI units. If so
then weight is m g in NEWTONS where m is in Kilograms and g is about 9.81 meters/ second^2
if so
weight = 0.075 kg * 9.81 m/s^2 = 0.736 Newtons
To calculate the weight of the rule, we need to use the principle of moments. The principle of moments states that the sum of the clockwise moments is equal to the sum of the anticlockwise moments.
In this case, the clockwise moment is caused by the weight of the rule, and the anticlockwise moment is caused by the hanging mass. We can set up the equation as follows:
(clockwise moment) = (anticlockwise moment)
The weight of an object is given by the formula:
Weight = mass × gravitational acceleration
First, we need to find the clockwise moment. Suppose the weight of the meter rule is W gram. The distance from the 30 cm mark to the zero mark is 30 cm. Therefore, the clockwise moment is W × 30.
The anticlockwise moment is given by the mass of the hanging weight multiplied by the distance from the zero mark to the point where it is hanging. The distance in this case is 30 cm (since it is hanging from the zero mark). So, the anticlockwise moment is 50g × 30 cm.
Setting up the equation:
W × 30 = 50g × 30 cm
To convert grams to kilograms, we divide by 1000:
W × 30 = 0.05 kg × 30 cm
To convert centimeters to meters, we divide by 100:
W × 30 = 0.05 kg × 0.3 m
Simplifying the equation:
W × 30 = 0.015 kg
Dividing both sides by 30:
W = 0.015 kg ÷ 30
Calculating:
W = 0.0005 kg
Therefore, the weight of the meter rule is 0.0005 kg.