A uniform metre rule of mass 100g balances horizontally on a knife-edge at the 40cm mark when a mass X is placed at the 20cm mark. Calculate the value of X.
To calculate the value of X, we can use the principle of moments. The principle of moments states that for an object to be in equilibrium, the sum of the clockwise moments must be equal to the sum of the anticlockwise moments.
In this case, the metre rule is balanced on the knife-edge, so the clockwise moments and anticlockwise moments must be equal.
The mass of the metre rule is given as 100g. To calculate the moment of the metre rule about the knife-edge, we need to multiply the mass by its distance from the knife-edge. In this case, the distance is (40 cm - 0 cm) = 40 cm.
The moment of the metre rule is therefore: Moment of metre rule = mass × distance
Moment of metre rule = 100g × 40cm
Now, when the mass X is placed at the 20cm mark, it creates an anticlockwise moment. Let's assume the mass X is placed at a distance of d cm from the knife-edge.
The moment of the mass X is: Moment of mass X = mass X × distance
Moment of mass X = X × d cm
According to the principle of moments, the clockwise and anticlockwise moments are equal, so we have:
Moment of metre rule = Moment of mass X
100g × 40cm = X × d cm
From the given information, we know that the metre rule balances, so the sum of the clockwise moments and anticlockwise moments is zero. Therefore, we can say:
Clockwise moments = Anticlockwise moments
Moment of metre rule - Moment of mass X = 0
100g × 40cm - X × d cm = 0
Now, we can substitute the known values of mass and distance into the equation to solve for X:
100g × 40cm - X × d cm = 0
4000g.cm - X × d cm = 0
Since the metre rule is balanced, the sum of the moments is zero. We also know that the metre rule is balanced at the 40cm mark when mass X is placed at the 20cm mark. So, the distance d can be calculated as:
d = 40cm - 20cm
d = 20cm
Substituting this value into the equation:
4000g.cm - X × 20cm = 0
Now we can solve for X:
X × 20cm = 4000g.cm
X = 4000g.cm / 20cm
Calculating the value of X:
X = 200g
Therefore, the value of X is 200g.
the mass of the rule acts at the center of mass (50cm)
X * 20cm = 100g * 10cm