...carries a ring which slides upon the rod. The rod is suspended by means of the string from a smooth peg ; prove that if 6 be the angle which the rod makes with the horizon, then tan 0 = 3~i - 3~*. 76. If two forces acting along chords of a circle are inversely proportional...

...; and prove that, if in this position the rod and string be equally inclined to the vertical, 1250. A uniform rod, of length c, rests with one end on...distance h from the centre of the ellipse; prove that, if 0 be the angle made by the rod with the horizon, tan 0 = -^r tan <f>, where a cos <£ + h = c cos 0....

...weight which slides on the rod. The rod is suspended by means of the string from a smooth peg ; shew that if 6 be the angle which the rod makes with the horizon, then tan 6 = 3~^ — 3~^. 23. A square rests with its plane perpendicular to a smooth wall, one corner...

...+ az- ex z + bx — ay MATHEMATICAL PHYSICS. \st October, 1874—Morning. Professor ENGLAND, MA 1. A uniform rod of length c rests with one end on a smooth elliptic arc, whose axis major is horizontal, and with the other on a smooth vertical plane at a distance h from the centre...

...with the vertical when in equilibrium is given by the equation 2c cos 16 — b cos 0 - a sin 0. 2260. A uniform rod, of length c, rests with one end on...with the horizon and 2a, 26 the axes of the ellipse, 25 tan 6 = a, tan <j>, where a cos <f> + k = c cos 0 ; and explain the result when a = 26 = c, h =...

...light ring which slides upon the rod. The rod is suspended by means of the string from a smooth peg; prove that if 6 be the angle which the rod makes with the horizon, then tan 0 = 3~*-3~3. [Math. Tripos, 1852.] Ex. 10. A heavy uniform rod of length 2a turns freely on...