$\begin{array}{1 1}(a)\;\large\frac{\pi}{3}\;\normalsize cm&(b)\;\large\frac{25\pi}{3}\;\normalsize cm\\(c)\;\large\frac{5\pi}{3}\;\normalsize cm&(d)\;\large\frac{7\pi}{3}\;\normalsize cm\end{array}$

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Here radius of the circle $r=\large\frac{50}{2}$

$\qquad\qquad\qquad\qquad\quad=25cm$

Let $O$ be the centre of the circle and AB be the given chord such that $AB=25cm$

Now $OA=OB=r=25cm$

$AB=25cm$

$\Delta OAB$ is equilateral.

$\angle AOB=60^{\large\circ}$

$\quad\quad\;\;=\big(60\times \large\frac{\pi}{180}\big)$$radians$

$\quad\quad\;\;=\large\frac{\pi}{3}$$radians$

Let the length of the minor arc of chord AB be $l$ then

$l=r\theta$

$\;\;=25\times \large\frac{\pi}{3}$

$\;\;=\large\frac{25\pi}{3}$$cm$

Hence (b) is the correct answer.

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