A METER RULE IS FOUND TO BALANCE AT ITS 49CM MARK WHEN A MASS OF 100G IS SUSPENDED AT ITS 10CM MARK IT BALANCED AT THE 36CM ,CALCULATE THE WEIGHT OF THE RULE.
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To calculate the weight of the rule, we can 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.
Let's assign variables to the unknowns and given values:
Length of the meter rule = L (in cm)
Distance from the 49 cm mark to the fulcrum = x (in cm)
Distance from the 10 cm mark to the fulcrum = y (in cm)
Weight of the rule = W (in g)
Given:
When a mass of 100g is suspended at the 10cm mark, it balances at the 36 cm mark.
Therefore, the clockwise moment is equal to the anticlockwise moment.
Clockwise moment = 100g * y
Anticlockwise moment = W * (L - x)
It is also given that the meter rule balances at its 49cm mark when a mass of 100g is suspended at its 10cm mark.
Therefore, the clockwise moment is equal to the anticlockwise moment.
Clockwise moment = 100g * (49 - 10)
Anticlockwise moment = W * (L - 49)
Setting up the equation:
100g * y = W * (L - x) (Equation 1)
100g * (49 - 10) = W * (L - 49) (Equation 2)
Now we can solve the equations simultaneously to find the value of W.
From Equation 1:
100g * y = W * (L - x)
From Equation 2:
100g * (49 - 10) = W * (L - 49)
Substituting the given values:
90g = W * (L - 49)
We can now solve for W:
W = 90g / (L - 49)
Please provide the length of the meter rule (L in cm) so that we can compute the weight of the rule.
To calculate the weight of the meter rule, we will use the principle of moments. The principle of moments states that the sum of the moments acting on an object is zero when it is in equilibrium.
Let's assume the weight of the meter rule is W grams. We also have two known points of balance:
1. When a mass of 100g is suspended at the 10cm mark, the rule balances at the 36cm mark.
2. When the rule is balanced at its 49cm mark.
Using the principle of moments, we can calculate the weight of the rule.
First, we need to find the distance from the 49cm mark to the 10cm mark, which is 49cm - 10cm = 39cm.
Now, let's calculate the moments:
Moment of the 100g mass = 100g × 36cm
Moment of the rule weight = W × 39cm
Since the rule is balanced, the moments from the mass and the rule weight must cancel each other out. Therefore, we have the equation:
100g × 36cm = W × 39cm
Simplifying the equation:
3600g cm = 39W g cm
Dividing both sides by 39cm:
3600g / 39 = W g
Approximating:
92.31g = W g
Therefore, the weight of the meter rule is approximately 92.31 grams.