A particle of mass m is attached to an end of a light rigid rod of length a. The other end of the rod is fixed, so that the rod can rotate freely in vertical plane about its fixed end. The mass m is given a horizontal velocity u at the lowest point. (a) Prove that when the radius to the mass makes an angle `theta` with the upward vertical the horizontal component of the acceleration of the mass (measured in direction of u) is `[g(2+3 cos theta)-u^(2)//a] sin theta` (b) If 4ag lt`u^(2)` lt5ag, show that there are four points at which horizontal component of acceleration is zero. locate the points.
