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If a semicircular annular ring of inner radius of 10\; cm and the position of the center of mass from the base is 9.90\; cm. Find the approximate value of outer radius (in cm) of the semicircular annular ring. If the ring have total mass equal to 10\; kg and surface density 10gm/cm^{2}

Option: 1 15

Option: 2 13

Option: 3 12

Option: 4 20

Answers (1)

best_answer

 

 As we know that the position of the center of mass of the semicircular annular ring is-  y_{cm}=\frac{4}{3\pi }\ast \frac{\left ( R^{3}_{2}-R^{3}_{1} \right )}{\left ( R^{2}_{2}-R^{2}_{1}\right )}

 

Now, y_{cm}=9.90\; cm and R_{1}=\; 10cm, so after putting these values in the above formula we can find that-

            R_{2}=20\; cm            

So, option (d) is correct.

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Gunjita

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