problem as shown in the pic, plz answer both parts! Bead on a hoop A bead of mas

Question

problem as shown in the pic, plz answer both parts!

Bead on a hoop A bead of mass m is constrained to move on a frictionless hoop of radius r that is located a distance R from an object of mass M. Assume R >> r, and assume that M is much larger than the mass of the hoop, which is much larger than m. (a)If the hoop is held fixed and the bead is released from the top point, as shown what is its speed when it gets to the rightmost point on the hoop? If the hoop is released and the bead starts at a point just slightly to the right of the top point, what is its speed with respect to the hoop when it gets to the rightmost point on the hoop? Assume that you grab M and move it to the right to keep it a distance R from the hoop.

Explanation / Answer

a)mv^2/R=GMm/R^2

SO V=root under(GM) Ans...........

b)in this case distance =(R-r)

so mv^2/(R-r)=GMm/(R-r)^2

so v=root under(GM/(R-r)) Ans................

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