A metre rule is balanced on a knife edge at 55cm mark when a mass of 40g is hung from 95cm maqrk. Find the mass of the ruler?
m * (55-50) = 40 * (95-55)
Answer pls
To solve this problem, we can apply the principle of moments, which states that the sum of clockwise moments is equal to the sum of anticlockwise moments when an object is in equilibrium.
First, let's define some variables:
- Mass of the ruler: M (to be determined)
- Distance from the center of mass of the ruler to the 55cm mark: x (45cm)
- Distance from the center of mass of the ruler to the 95cm mark: d (5cm)
- Mass hung from the 95cm mark: m (40g)
Now, let's calculate the moments on each side of the knife edge:
1. Clockwise moment (due to the mass at the 55cm mark):
Moment = M * x
Moment = M * 45cm
2. Anti-clockwise moment (due to the mass at the 95cm mark):
Moment = m * d
Moment = 40g * 5cm
Moment = 200g cm
Since the ruler is balanced, the clockwise moment is equal to the anticlockwise moment. Therefore:
M * 45cm = 200g cm
Since 1g = 0.001kg, we can convert the mass and rearrange the equation to solve for M:
M * 45cm = 200 * 0.001kg * 9.8m/s^2 * 100cm
M * 45cm = 196N/cm
Dividing both sides of the equation by 45cm:
M = 196N/cm / 45cm = 4.36N
Therefore, the mass of the ruler is approximately 4.36 kg.
To find the mass of the ruler, we can use the principle of moments, which states that the sum of the clockwise moments is equal to the sum of the anticlockwise moments when an object is in equilibrium.
Let's break down the given information into moments:
Clockwise moment:
Mass of the ruler x Distance of the ruler's center of mass from the knife edge
Anticlockwise moment:
Mass of the hanging mass x Distance of the hanging mass from the knife edge
Since the ruler is balanced, the moments on both sides will be equal. Let's denote the mass of the ruler as M, and the distance from the ruler's center of mass to the knife edge as D.
Clockwise moment: M × D = Anticlockwise moment: 40g × (95cm - 55cm)
Now, we need to convert the given distances into meters, as the SI unit is used in physics calculations.
55cm = 0.55m
95cm = 0.95m
Substituting the values into the equation:
M × D = 40g × (0.95m - 0.55m)
Simplifying:
M × D = 40g × 0.4m
M × D = 16g·m
Now, we need to find the value of D, the distance from the ruler's center of mass to the knife edge. In this case, it is given as 55cm, which is equivalent to 0.55m.
Substituting the value of D:
M × 0.55m = 16g·m
Dividing both sides by 0.55m:
M = 16g·m / 0.55m
M = 29.09g
Therefore, the mass of the ruler is approximately 29.09 grams.