It is found that a uniform metre rule of mass 50g can be balanced on a knife-edge when a mass of 20g is hung 20cm from one end of the rule how far from the centre of gravity of the metre rule is the knife-edge
To find the distance from the center of gravity of the meter rule to the knife-edge, we can use the principle of moments.
The principle of moments states that for an object to be in equilibrium, the sum of the anti-clockwise moments about any point must be equal to the sum of the clockwise moments about the same point.
In this case, we can consider the center of gravity of the meter rule as the reference point.
Let's denote the distance from the center of gravity to the knife-edge as 'x'.
The clockwise moment is given by the product of the mass of the rule (50g) and the distance from the center of gravity to the knife-edge (x).
The anti-clockwise moment is given by the product of the hanging mass (20g) and the distance from the hanging mass to the center of gravity of the rule (20cm).
Since the meter rule is balanced, the sum of the anti-clockwise moments is equal to the sum of the clockwise moments.
So we can set up the following equation:
20g * 20cm = 50g * x
Now, let's convert the units for calculation purposes:
20g * 0.2m = 50g * x
4g = 50g * x
To find the value of 'x', we can rearrange the equation:
x = 4g / 50g
x = 0.08m
Therefore, the knife-edge is located 0.08 meters (or 8 cm) from the center of gravity of the meter rule.