A uniform meter rule of mass 95g can be balance horizontally on a knife-edge when a mass of 5g is suspended 10cm from one end. Calculate the distance of the knife-edge from the center of the rule.
To calculate the distance of the knife-edge from the center of the rule, we can make use of the principle of moments.
The principle of moments states that for a body in rotational equilibrium, the sum of the anticlockwise moments is equal to the sum of the clockwise moments.
In this case, the anticlockwise moment is produced by the mass of the rule itself, and the clockwise moment is produced by the suspended mass.
We can find the moments using the formula:
Moment = force × distance
Let's assign variables to the given quantities:
- Mass of the rule = m1 = 95g = 0.095kg
- Mass suspended = m2 = 5g = 0.005kg
- Distance of suspended mass = d2 = 10cm = 0.1m
- Distance of knife-edge from the center = x (unknown)
Since the ruler is balanced horizontally, the total moment on one side is equal to the total moment on the other side:
Moment anticlockwise = Moment clockwise
m1 × g × x = m2 × g × d2
where g is the acceleration due to gravity (approximately 9.8 m/s²).
Simplifying the equation by dividing both sides by g:
m1 × x = m2 × d2
Now, substituting the values:
0.095kg × x = 0.005kg × 0.1m
0.095x = 0.0005
Divide both sides by 0.095:
x = 0.0005 / 0.095 ≈ 0.0053 m
Therefore, the distance of the knife-edge from the center of the rule is approximately 0.0053 meters, or 5.3 mm.