A uniform half meter scale is balanced at 60 cm mark.when weight of 10 gf and 30 gf are suspended at 20 cm and 90 cm mark respectively calculate the weight of scale
Half meter scale can not be balanced at 60 cm.
It's of 50 cm only.
To calculate the weight of the scale, we need to find the moment caused by the weights of 10 gf and 30 gf.
The moment of a force is calculated by multiplying the force by the perpendicular distance from the fulcrum (balance point). In this case, the balance point is at the 60 cm mark.
Let's calculate the moments:
Moment caused by 10 gf weight:
Moment1 = 10 gf * (60 cm - 20 cm) = 10 gf * 40 cm = 400 gf·cm
Moment caused by 30 gf weight:
Moment2 = 30 gf * (90 cm - 60 cm) = 30 gf * 30 cm = 900 gf·cm
Since the scale is in equilibrium (balanced), the sum of the moments on each side of the balance point should be equal.
Moment1 + Moment2 = Weight of Scale * (distance from fulcrum to weight of scale)
Let's denote the weight of the scale as W:
400 gf·cm + 900 gf·cm = W * (60 cm - 60 cm)
1300 gf·cm = 0 gf·cm
Since the left side of the equation is not equal to the right side, this means there is an error in the information provided. Please recheck the values and distances given for the weights on the scale so we can provide an accurate calculation.
To calculate the weight of the scale, we need to consider the principle of moments. According to this principle, if an object is in equilibrium (balanced), the sum of the clockwise moments is equal to the sum of the anticlockwise moments.
In this case, the weight of the scale can be considered as a single force acting on the midpoint of the scale. Since the scale is balanced at the 60 cm mark, the distance between this midpoint and the two weights (10 gf and 30 gf) can be calculated.
Let's calculate the distances first:
Distance of 10 gf weight from the 60 cm mark = 60 cm - 20 cm = 40 cm
Distance of 30 gf weight from the 60 cm mark = 90 cm - 60 cm = 30 cm
Now, we can calculate the moments:
Moment of 10 gf weight = 10 gf × 40 cm = 400 gf·cm
Moment of 30 gf weight = 30 gf × 30 cm = 900 gf·cm
Since the scale is balanced, the clockwise moments should be equal to the anticlockwise moments:
Clockwise moment = Anticlockwise moment
Weight of the scale × Distance from the 60 cm mark = (Moment of 10 gf weight) + (Moment of 30 gf weight)
Let's substitute the values we have:
Weight of the scale × 0 cm = 400 gf·cm + 900 gf·cm
Weight of the scale × 0 cm = 1,300 gf·cm
Since any value multiplied by 0 is 0, we can ignore the term on the left side. Therefore:
1,300 gf·cm = Weight of the scale × 0 cm
Weight of the scale = 1,300 gf·cm / 0 cm
Since any value divided by 0 is undefined, we cannot determine the weight of the scale with the given information.