NAEST-2020: The centre of mass of a vibrating Chimta - posit

Question: NAEST-2020 Vibrating Chimta: The centre of mass of a vibrating Chimta
Question 1: In the beginning, the video shows a Chimta hanging from a rod. The centre of mass of the Chimta is

1. at the point where it touches the rod
2. on the left prong
3. on the right prong
4. none of these

Question 2: In the later part of the video, the chimta is vibrated. Assume that the chimta vibrates symmetrically about the vertical line through its contact with the rod. Let the frequency of vibration be n.The centre of mass of the Chimta

1. vibrates with frequency n
2. vibrates with frequency 2n
3. vibrates with frequency n / 2
4. does not vibrate

Solution 1: The Chimta is symmetric about the vertical line passing through the hanging point. The centre of mass will lie on this line somewhere in the middle of the chimta. If the length of the chimta is L then centre of mass will be approximately L/2 distance below the hanging point. Hence, option (4) is correct.

Solution 2: There is no external force on the Chimta in the horizontal direction. Thus, centre of mass of the Chimta remains fixed (does not vibrate). The left and the right prongs move outwards or inwards in phase keeping the centre of mass fixed. Hence, option (4) is correct.

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