Problem Statement | A marble travels in a circular path of radius R at a constant speed and height around the inside of a bowl, as pictured. The bowl and marble are on a planet with an unknown value of g. The friction between the side of the bowl and the marble is negligible. The side of the bowl makes an angle, 8, with respect to the vertical and the marble takes T seconds to make one full rotation around the bowl. (a) Find an expression for the radius, R, of the marble's path around the bowl in terms of numbers, , T, 8, and g only. (hint: notice that the mass of the marble, m, does not appear in this statement! Hint 2: an example answer is R = 31 g sin(0)/T, this is not the correct answer!) (b) Do the units or dimensions of your answer match what you expect them to be? Explain.

Problem Statement | A marble travels in a circular path of radius R at a constant speed and height around the inside of a bowl, as pictured. The bowl and marble are on a planet with an unknown value of g. The friction between the side of the bowl and the marble is negligible. The side of the bowl makes an angle, 8, with respect to the vertical and the marble takes T seconds to make one full rotation around the bowl. (a) Find an expression for the radius, R, of the marble's path around the bowl in terms of numbers, , T, 8, and g only. (hint: notice that the mass of the marble, m, does not appear in this statement! Hint 2: an example answer is R = 31 g sin(0)/T, this is not the correct answer!) (b) Do the units or dimensions of your answer match what you expect them to be? Explain.