a metre rule is found to balance horizontally at 48cm mark .when a body of mass 60g is suspended at d 6cm mark ,the balance point is found to be the 30cm mark .calculate the mass of the metre rule and distance of the balance point from zero end if the body were moved to the 13 cm mark .
To solve this problem, we need to use the principle of moments. The principle of moments states that the sum of the clockwise moments about any point is equal to the sum of the anticlockwise moments about the same point.
Let's start by defining some variables:
m1 = mass of the body (60g)
l1 = length of the balance arm when the body is at the 6cm mark (30cm)
l2 = length of the balance arm when the body is at the 13cm mark (?)
L = length of the meter rule
First, let's find the mass of the meter rule:
The balance point is at the 48cm mark, which means that the center of mass of the meter rule is at that point. The distance of the center of mass from the zero end is given by L/2.
From the principle of moments, we have:
(m1 * l1) = (m2 * L/2)
Substituting the known values:
(60g * 30cm) = (m2 * L/2)
Now, let's find the distance of the balance point from the zero end when the body is at the 13cm mark:
Using the principle of moments again:
(m1 * l1) = (m2 * l2)
Substituting the known values:
(60g * 30cm) = (m2 * 13cm + m2 * l2)
Now, let's solve the two equations simultaneously to find m2 and l2:
(60g * 30cm) = (m2 * L/2) -- Equation 1
(60g * 30cm) = (m2 * 13cm + m2 * l2) -- Equation 2
From Equation 1, we can solve for m2:
m2 = (60g * 30cm) / (L/2)
Then we can substitute this value into Equation 2:
(60g * 30cm) = ((60g * 30cm) / (L/2)) * 13cm + ((60g * 30cm) / (L/2)) * l2
From this equation, we can solve for l2:
l2 = [(60g * 30cm) - ((60g * 30cm) / (L/2)) * 13cm] / ((60g * 30cm) / (L/2))
Once you know the value of m2 and l2, you can calculate the mass of the meter rule (m2) and the distance of the balance point from the zero end (l2).