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 can treat it as two separate rods and find their individual center of masses.
First, consider the rod on the left side of the bend. This rod has a length of 1 meter (half the length of the entire rod). The center of mass of this rod is located at its midpoint, which is at a distance of 0.5 meters from the left end of the rod.
Next, consider the rod on the right side of the bend. This rod also has a length of 1 meter. The center of mass of this rod is also located at its midpoint, which is again at a distance of 0.5 meters from the left end of the rod.
Now, we have two separate center of masses, one for each of the two rods. To find the overall center of mass of the bent rod, we need to take into account the mass of each rod. The mass of the rod is assumed to be uniformly distributed along its length.
Since the rod is uniform, it has the same mass per unit length throughout. Let's assume the mass of the rod per unit length is m.
The total mass of the rod is then m * (length of the rod) = m * 2 meters.
Now, to find the overall center of mass, we can use the concept of weighted average.
The x-coordinate of the overall center of mass, denoted as Xcm, can be calculated as:
Xcm = (m1*x1 + m2*x2) / (m1 + m2),
where m1 is the mass of the left rod, m2 is the mass of the right rod, x1 is the x-coordinate of the center of mass of the left rod, and x2 is the x-coordinate of the center of mass of the right rod.
In this case, m1 = m * 1 meter (mass of the left rod) and x1 = 0.5 meters (x-coordinate of the center of mass of the left rod).
Similarly, m2 = m * 1 meter (mass of the right rod) and x2 = 1.5 meters (x-coordinate of the center of mass of the right rod).
Substituting the values into the formula, we get:
Xcm = (m * 1 meter * 0.5 meters + m * 1 meter * 1.5 meters) / (m * 1 meter + m * 1 meter)
= (0.5 + 1.5) / 2
= 1 meter.
Therefore, the x-coordinate (or position) of the center of mass of the bent rod is 1 meter from the left end of the rod.