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What is the distance of centre of mass o...

What is the distance of centre of mass of a half fring from centre if the ring has radius `=0.5` m [XI]

A

`1/pi`

B

`(1)/(3pi)`

C

`(2)/(3pi)`

D

`(1)/(2pi)`

Text Solution

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The correct Answer is:
To find the distance of the center of mass of a half ring from the center of the ring, we can follow these steps: ### Step 1: Understand the Geometry We have a half ring (semicircular) with a radius \( r = 0.5 \) m. The center of mass of a half ring lies along the axis of symmetry of the semicircle. ### Step 2: Use the Formula for Center of Mass The distance \( y \) of the center of mass of a half ring from the center of the ring is given by the formula: \[ y = \frac{2r}{\pi} \] where \( r \) is the radius of the half ring. ### Step 3: Substitute the Given Radius Substituting the given radius \( r = 0.5 \) m into the formula: \[ y = \frac{2 \times 0.5}{\pi} \] ### Step 4: Simplify the Expression Calculating the numerator: \[ y = \frac{1}{\pi} \] ### Step 5: Final Result Thus, the distance of the center of mass of the half ring from the center of the ring is: \[ y = \frac{1}{\pi} \text{ meters} \]
To find the distance of the center of mass of a half ring from the center of the ring, we can follow these steps: ### Step 1: Understand the Geometry We have a half ring (semicircular) with a radius \( r = 0.5 \) m. The center of mass of a half ring lies along the axis of symmetry of the semicircle. ### Step 2: Use the Formula for Center of Mass The distance \( y \) of the center of mass of a half ring from the center of the ring is given by the formula: \[ ...
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