A thin uniform rod of length 2m is bent at 90 degree angle from the mid point . find the centre of mass of bent road
To find the center of mass of the bent rod, we need to consider the individual center of masses of the two segments formed by the bend.
Let's say the bent rod is divided into two segments, AB and BC, where A and C are the ends of the rod and B is the bend point. We can assume that the rod has a uniform mass distribution.
First, let's find the center of mass of segment AB. The center of mass of a uniform rod is located at its midpoint. Since AB has a length of 1 meter, its center of mass is located at a distance of 0.5 meters from point A.
Next, let's find the center of mass of segment BC. Since BC is also a uniform rod with a length of 1 meter, its center of mass is also located at a distance of 0.5 meters from point B.
To determine the location of the center of mass of the bent rod, we can calculate the weighted average of the two centers of masses of segments AB and BC. Since segment AB and segment BC have equal lengths, their weights will also be equal.
Let's denote the location of the center of mass of the bent rod as P. We can use the formula for the weighted average:
P = (m₁ * x₁ + m₂ * x₂) / (m₁ + m₂),
where m₁ and m₂ are the masses of segments AB and BC respectively, and x₁ and x₂ are the distances of their center of masses from the bend point B.
Since the rod has a uniform mass distribution, the masses of segments AB and BC will be equal. Let's call this mass 'm'. Therefore, the formula simplifies to:
P = (m * 0.5 + m * 0.5) / (m + m).
Simplifying further:
P = (m + m) / (2m).
Canceling the common factors:
P = 1 / 2.
So, the center of mass of the bent rod is located at a distance of 0.5 meters from the bend point B.