A uniform rod of mass \(m\) and length \(2a\) is inclined at an angle \(\theta\) to the vertical and falls without rotation so as to impinge with velocity \(u\) on a perfectly rough inelastic horizontal plane. Determine the impulsive force on the rod. \par Show also that when the rod becomes horizontal the impulse imparted to the plane is \(\frac{2}{3}m\sqrt{(u^2\sin^2\theta + \frac{3}{4}ag\cos\theta)}\).