A metre rule is found to balance at the 35cm mark. when a body of mass 50kg is suspended at the 10cm mark, the balance point is found to be at 20cm mark find
a)the Mass of the ruler.
To find the mass of the ruler, we can set up an equation using the principle of moments. The principle of moments states that the sum of the moments about any point in equilibrium is zero.
Let's consider the moments acting on the ruler when it is balanced at the 35 cm mark. The moment due to the weight of the ruler can be calculated as the product of its mass and the distance from the point of rotation (the 35 cm mark) to the center of mass of the ruler.
In this case, the moment due to the weight of the ruler is zero since the ruler is balanced. Therefore, we can set up the equation as follows:
Mass of the ruler * distance to the center of mass = Weight of the body * distance
Since the weight of the body (50 kg) is suspended at the 10 cm mark and creates a balance point at the 20 cm mark, the distance between the two weights is 10 cm.
Mathematically, the equation is:
Mass of the ruler * (35 cm - center of mass) = 50 kg * (20 cm - 10 cm)
Simplifying the equation:
Mass of the ruler * (35 cm - center of mass) = 50 kg * 10 cm
Now we can solve for the mass of the ruler.
Let's say the center of mass of the ruler is x cm. The equation becomes:
Mass of the ruler * (35 cm - x cm) = 50 kg * 10 cm
Now, we need additional information to find the center of mass of the ruler.