A METRE RULE IS BALANCED BY MASSES OF 24 G AND 16 G SUSPENDED FROM ITS ENDS. FIND THE POSITION OF ITS PIVOT.
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To find the position of the pivot on a meter rule balanced by masses of 24 g and 16 g suspended from its ends, 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 any point must be equal to the sum of the anticlockwise moments about the same point.
Let's assume that the pivot is to the left of the 24 g mass and to the right of the 16 g mass, and that the distances of the masses from the pivot are x and y, respectively.
The moment (M) of the 24 g mass about the pivot is given by:
M1 = 24 g * x
The moment (M) of the 16 g mass about the pivot is given by:
M2 = 16 g * y
Since the meter rule is balanced, M1 must be equal to M2:
M1 = M2
Therefore, we have:
24 g * x = 16 g * y
Now we can calculate the position of the pivot by substituting the values.
Given:
Mass of the 24 g = 24 g
Mass of the 16 g = 16 g
Let's assume:
x = distance of the 24 g mass from the pivot
y = distance of the 16 g mass from the pivot
We have the equation:
24 g * x = 16 g * y
Substituting the values, we get:
24 g * x = 16 g * y
24 x = 16 y
3 x = 2 y
Therefore, the position of the pivot is such that the distance of the 24 g mass from the pivot is three times the distance of the 16 g mass from the pivot.
To find the position of the pivot of the metre rule, we need to determine the point where it is balanced by the masses at its ends.
First, let's represent the masses and their positions on the metre rule:
Mass 1: 24 g (located at distance x1 from the pivot)
Mass 2: 16 g (located at distance x2 from the pivot)
For the metre rule to be balanced, the sum of the anticlockwise moments must be equal to the sum of the clockwise moments.
The moment of a force is calculated by multiplying the force by the perpendicular distance from the point of rotation (pivot) to the line of action of the force.
In this case, the clockwise moment is created by Mass 1, and the anticlockwise moment is created by Mass 2.
The equation for this situation is:
(Clockwise Moment) = (Anticlockwise Moment)
(Force of Mass 1 × Distance x1) = (Force of Mass 2 × Distance x2)
(24 g × x1) = (16 g × x2)
Now, to find the position of the pivot, we can solve for x1 by rearranging the equation:
x1 = (16 g × x2) / (24 g)
Simplifying further:
x1 = (2/3) x2
Therefore, the position of the pivot is 2/3 of the distance from Mass 2 to Mass 1.