A metre rule is balanced by masses of 24g and 16g from its ends.Find the position of its pivot.
mark on metre stick ---- x
24x = 16(100-x)
24x = 1600 - 16x
40x = 1600
x = 40
the pivot is on the 40 cm mark of the metre stick
40cm
To find the position of the pivot of the meter rule, we need to consider the moments of the two masses acting on the rule.
Let's assume that the length of the meter rule is L and the position of the pivot from one end is x.
The moment of a force is calculated by multiplying the magnitude of the force by the perpendicular distance to the pivot point.
The 24g mass is located at one end of the meter rule, so its moment is (0.024 kg) * (L - x). Similarly, the moment of the 16g mass is (0.016 kg) * (x).
For the meter rule to be balanced, these two moments must be equal:
(0.024 kg) * (L - x) = (0.016 kg) * (x)
Now let's solve this equation to find the position of the pivot x:
0.024L - 0.024x = 0.016x
0.040x = 0.024L
x = (0.024L) / 0.040
x = 0.6L
Therefore, the position of the pivot from one end of the meter rule is 0.6 times the total length L.
To find the position of the pivot of the meter rule, we need to consider the moments on both sides of the pivot.
A moment is calculated by multiplying the mass by its distance from the pivot. The equilibrium condition states that the sum of clockwise moments must be equal to the sum of anticlockwise moments.
Let's assume the distance of the pivot from one end of the meter rule is x.
On one side of the pivot, we have the 24g mass with a moment of (24g)*(x). On the other side, we have the 16g mass with a moment of (16g)*(100 - x), where 100 is the length of the meter rule in centimeters.
So, the equation for equilibrium is:
(24g)*(x) = (16g)*(100 - x)
Now, we can solve this equation to find the value of x, which will give us the position of the pivot.
Expanding the equation, we have:
24gx = 16g(100 - x)
Simplifying, we get:
24x = 1600 - 16x
Combining like terms:
40x =1600
Dividing both sides by 40:
x = 40
Therefore, the position of the pivot is 40 cm from the end of the meter rule where the 24g mass is placed.