Q3. A small bead, of mass m, is suspended from a fixed-point O by a light inextensible string of length a. With the string taut, the bead is at the point B, vertically below O, when it is set into vertical circular motion with an initial horizontal velocity u, as shown in the diagram. The string does not become slack in the subsequent motion. The velocity of the bead at the point A, where A is vertically above O, is v. (a) Show that y2 = u²-4ag. (b) The ratio of the tensions in the string when the bead is at the two points A and B is 2: 5. Find u in terms of g and a. B 11
Q3. A small bead, of mass m, is suspended from a fixed-point O by a light inextensible string of length a. With the string taut, the bead is at the point B, vertically below O, when it is set into vertical circular motion with an initial horizontal velocity u, as shown in the diagram. The string does not become slack in the subsequent motion. The velocity of the bead at the point A, where A is vertically above O, is v. (a) Show that y2 = u²-4ag. (b) The ratio of the tensions in the string when the bead is at the two points A and B is 2: 5. Find u in terms of g and a. B 11
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Q3. A small bead, of mass m, is suspended from a fixed-point O by a light inextensible string of
length a. With the string taut, the bead is at the point B, vertically below O, when it is set into
vertical circular motion with an initial horizontal velocity u, as shown in the diagram.
The string does not become slack in the subsequent motion. The
velocity of the bead at the point A, where A is vertically above O, is v.
(a)
Show that v² = u² - 4ag.
(b)
The ratio of the tensions in the string when the bead is at the
two points A and B is 2: 5.
Find u in terms of g and a.
A
B
U
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