A uniform rod of 1 meter is bent at its midpoint to make90.The distance from its centre of mass
17.68
To find the distance from the center of mass of a uniform rod that has been bent at its midpoint, you can follow these steps:
1. Determine the position of the center of mass of the original uniform rod. In a uniform rod, the center of mass is located exactly at the midpoint. This means that the distance from either end of the rod to the center of mass is half the length of the rod.
2. After bending the rod to make a 90-degree angle, the center of mass position may change. The new distance from the center of mass can be determined by using the concept of moment of inertia.
3. The moment of inertia of an object is a measure of its resistance to rotational motion. It depends on the mass distribution of the object. For a uniform rod, the moment of inertia is given by the equation I = (1/12) * m * L^2, where I is the moment of inertia, m is the mass of the rod, and L is the length of the rod.
4. Since the rod is bent at the midpoint, it can be divided into two equal halves. Each half will have a length of 0.5 meters. Therefore, the moment of inertia of each half can be calculated individually.
5. Calculate the moment of inertia for each half of the rod using the formula I = (1/12) * m * L^2. Since each half has a length of 0.5 meters, substitute L = 0.5 into the equation. The mass of each half of the rod will depend on the overall mass distribution, but since the rod is uniform, the mass is also divided equally between the two halves.
6. Add the moment of inertia values from the two halves of the rod to get the total moment of inertia, I_total.
7. The distance from the center of mass to one end of the rod can be calculated by using the equation I_total = m * distance^2, where m is the total mass of the rod. Rearrange the equation to solve for the distance. This will give you the distance from the center of mass to one end of the rod.
Note: The exact calculations for the distances will depend on the mass distribution of the rod, but following these steps will guide you in finding the distances from the center of mass after the rod has been bent.