The distance between the vertex and the center of mass of a uniform solid planar circular segmen...

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The distance between the vertex and the center of mass of a uniform solid planar circular segment of angular size \( \theta \) and radius \( R \) is given by
[KVPY 2015]
(a) \( \frac{4}{3} R \frac{\sin (\theta / 2)}{\theta} \)
(b) \( R \frac{\sin (\theta / 2)}{\theta} \)
(c) \( \frac{4}{3} R \cos \left(\frac{\theta}{2}\right) \)
(d) \( \frac{2}{3} R \cos (\theta) \)
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