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A uniform circular disc has a radius of ...

A uniform circular disc has a radius of 20cm. A circular disc of radius 10cm is cut concentrically from the original disc. The shift in centre of mass is

A

`(1)/(200)cm`

B

`(7)/(300)cm`

C

`(1)/(400)cm`

D

zero

Text Solution

AI Generated Solution

The correct Answer is:
To find the shift in the center of mass when a smaller disc is cut from a larger disc, we can follow these steps: ### Step-by-Step Solution: 1. **Identify the Dimensions**: - The radius of the original disc (R) = 20 cm. - The radius of the cut-out disc (r) = 10 cm. 2. **Calculate the Area of Both Discs**: - Area of the original disc (A1) = πR² = π(20 cm)² = 400π cm². - Area of the cut-out disc (A2) = πr² = π(10 cm)² = 100π cm². 3. **Determine the Mass of Each Disc**: - Assuming uniform density (ρ), the mass of the original disc (M1) is proportional to its area: M1 = ρ * A1 = ρ * 400π. - The mass of the cut-out disc (M2) is: M2 = ρ * A2 = ρ * 100π. 4. **Calculate the Center of Mass of the Remaining Shape**: - The center of mass of the original disc is at its center (0,0). - The center of mass of the cut-out disc is also at (0,0) since it is concentric. - The remaining shape after cutting out the smaller disc is symmetric about the center. 5. **Determine the Shift in Center of Mass**: - Since both the original disc and the cut-out disc are symmetric and concentric, the center of mass of the remaining shape does not change. - Therefore, the shift in the center of mass is zero. 6. **Conclusion**: - The shift in the center of mass after cutting out the smaller disc is **0 cm**. ### Final Answer: The shift in the center of mass is **0 cm**. ---
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