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 :
Which of the following microbes is NOT involved in the preparation of household products?
A. \(\textit{Aspergillus niger}\)
B. \(\textit{Lactobacillus}\)
C. \(\textit{Trichoderma polysporum}\)
D. \(\textit{Saccharomyces cerevisiae}\)
E. \(\textit{Propionibacterium sharmanii}\)
A sphere of radius R is cut from a larger solid sphere of radius 2R as shown in the figure. The ratio of the moment of inertia of the smaller sphere to that of the rest part of the sphere about the Y-axis is :