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A uniform straight rod is placed in vert...

A uniform straight rod is placed in vertical position on a smooth horizontal surface and released. As the rod is in motion, the centre of mass moves

A

the centre of rod follows straight line path

B

the centre mass follows circular path

C

the instantaneous axis is passing through the contact point

D

all of above

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem step by step, we need to analyze the motion of the uniform straight rod when it is released from a vertical position on a smooth horizontal surface. ### Step 1: Understand the Initial Setup - A uniform straight rod of length \( L \) is placed vertically on a smooth horizontal surface. - The center of mass of the rod is located at a distance of \( \frac{L}{2} \) from the base of the rod. **Hint:** Visualize the rod standing vertically with its center of mass at the midpoint. ### Step 2: Identify Forces Acting on the Rod - The only force acting on the rod is its weight, which is \( mg \) (where \( m \) is the mass of the rod and \( g \) is the acceleration due to gravity). - Since the surface is smooth, there is no friction acting on the rod. **Hint:** Remember that the absence of friction means there is no horizontal force acting on the rod. ### Step 3: Analyze the Motion of the Rod - When the rod is released, it will start to fall due to gravity. - The center of mass of the rod will move downward as the rod falls. **Hint:** Consider the motion of the center of mass as if it were a particle falling under the influence of gravity. ### Step 4: Determine the Path of the Center of Mass - As the rod falls, the center of mass will follow a straight vertical path downward. - This is because the rod is not experiencing any horizontal forces, and thus the motion of the center of mass can be treated as free fall. **Hint:** Think of the center of mass as a point mass falling freely under gravity. ### Step 5: Conclusion - The path followed by the center of mass of the rod is a straight line downward, similar to the motion of a freely falling object under gravity. **Final Answer:** The path followed by the center of mass of the rod is a straight line.
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