51. In Larry Niven's science-fiction novel Ringworld, a rigid ring of material rotatesabout a star (Fig. P13.51). The tangential speed of the ring is 1.25×10€ m/s, and itsradius is 1.53×10" m. (a) Show that the centripetal acceleration of the inhabitantsis 10.2 m/s?. (b) The inhabitants of this ring world live on the starlit inner surfaceof the ring. Each person experiences a normal contact force ñ. Acting alone, thisnormal force would produce an inward acceleration of 9.90 m/s2. Additionally, thestar at the center of the ring exerts a gravitational force on the ring and itsinhabitants. The difference between the total acceleration and the accelerationprovided by the normal force is due to the gravitational attraction of the centralstar. Show that the mass of the star is approximately 1032 kg.StarFFigure P13.51

Given that:Tangential speed of the ring, v=1.25×106 m/sRadius, r=1.53×1011 mInward acceleration due to normal force: an=9.90 m/s2a) Centripital acceleration:aC=v2r=(1.25×106)21.53×1011=10.2 m/s2 b) Difference in acceleration: ∆a=ac-an=10.2-9.90=0.3 m/s2Let the mass of the star is M.∆a=GMr2M=∆a×r2GM=0.3×(1.53×1011)2(6.67×10-11)=1.05×1032 Kg ≈1032 Kg

Answered: 51. In Larry Niven's science-fiction…