A uniform meter rule of mass 100g balance at 40cm mark a mass of p was placed at the 10cm mark find the value of p
To find the value of mass p placed at the 10cm mark on a uniform meter rule that balances at the 40cm mark, 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 about a point must be equal to the sum of the anticlockwise moments about the same point.
In this case, we can take the point of balance to be the 40cm mark. We need to find the value of mass p, which is located at the 10cm mark, so the distance between the weights is 40cm - 10cm = 30cm.
Let's assume the mass p is in grams.
The moment of an object is given by the product of its weight and the distance from the point of balance. Since the rule is uniform, we can assume that its weight acts at its center of mass, which is at the 50cm mark (halfway between the 40cm and 60cm marks).
Now, let's calculate the moments:
Clockwise moment = Weight of mass p × Distance of mass p from the point of balance
Anticlockwise moment = Weight of the ruler × Distance of the ruler from the point of balance
Using the principle of moments, we can set up the equation:
Clockwise moment = Anticlockwise moment
(mass p) × (10cm - 40cm) = (mass of the ruler) × (50cm - 40cm)
Simplifying the equation, we get:
-30 × p = 100 × 10
Now we can solve for p:
-30p = 1000
p = 1000 / -30
Evaluating p, we get:
p ≈ -33.33 grams
Therefore, the value of mass p placed at the 10cm mark is approximately -33.33 grams.