Length of cross belt connecting two pulleys of radii (r_{1}) and (r_{2}) and at a center distance

Question:

Length of cross belt connecting two pulleys of radii \(r_{1}\) and \(r_{2}\) and at a center distance \(D\) apart, is:

(a) \(\pi\left(r_{1}+r_{2}\right)+\left(r_{1}-r_{2}\right)^{2} / D+2 D\)

(b) \(\pi\left(r_{1}+r_{2}\right)+\left(r_{1}+r_{2}\right)^{2} / D+2 D\)

(c) \(\pi\left(r_{1}-r_{2}\right)+\left(r_{1}+r_{2}\right)^{2} / D+2 D\)

(d) \(\pi\left(r_{1}+r_{2}\right)+\left(r_{1}-r_{2}\right)^{2} / D+2 D\)

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