1) A body of mass 2 kg is tied to the end of a string 2 m long and revolved in a horizontal circle. If the breaking tension of the string is 400 N . calculate the maximum velocity of the body.

Sol: As per given in the question that, the body executes along horizontal direction, therefor centrifugal force will act on the body, which is balanced by centripetal force in form of tension in the string.
    So there will be two force along horizontal direction, and be balanced by each other.
   So the equation will be written as:
                                  Centrifugal force = Centripetal force  
                                      $$\begin{gathered} \frac{m{v_{max}}^2}{r} = T \\ where \\ m = mass of the body \\ {v}_{max} = maximum velocity of the body \\ r = radius of the circular path \\ T = tension in the string \\ putting the values as per the question: \\ \frac{2\times {v^2}_{max}}{2} = 400 \\ {v^2}_{max} = 400 \\ {v}_{max} = \sqrt{400} \\ {v}_{max} = 20 \raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right. :Ans \end{gathered}$$