A force defined by $ F = \alpha t^2 + \beta t $ acts on a particle at a given time $ t $. The factor which is dimensionless, if $ \alpha $ and $ \beta $ are constants, is:
A bob of heavy mass \(m\) is suspended by a light string of length \(l\). The bob is given a horizontal velocity \(v_0\) as shown in figure. If the string gets slack at some point P making an angle \( \theta \) from the horizontal, the ratio of the speed \(v\) of the bob at point P to its initial speed \(v_0\) is :