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We propose a spherically symmetric and anisotropic model for strange quark stars within the framework of MIT Bag model. Though the model is found to comply with all the physical requirements of a realistic star satisfying a strange matter equation of state (EOS), the estimated values the Bag constant for different strange star candidates like Her X-1, SAX J 1808.4-3658 and 4U 1820-30, clearly indicate that the Bag constant need not necessarily lie within the range of 60-80 MeV fm as claimed in the literature.

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