Question

A stone of mass 50 gm attached to one end of a 1.5 m long string is whirled in a vertical circle with a speed of 3m/s. If thr string makes an angle of 45 with the vertical then the tension in the string is

Answer 1

$$\begin{gathered} \mathrm{Given}, \\ \mathrm{Mass}\mathrm{of}\mathrm{the}\mathrm{stone},m=50\mathrm{g}=0.5\mathrm{kg} \\ \mathrm{Length}\mathrm{of}\mathrm{the}\mathrm{string},\mathit{}l=\mathrm{radius}\mathrm{of}\mathrm{vertical}\mathrm{circle},r=1.5\mathrm{m} \\ \mathrm{Velocity}\mathrm{of}\mathrm{the}\mathrm{stone},v=3\mathrm{m}{\mathrm{s}}^{-1} \\ \mathrm{Angle}\mathrm{of}\mathrm{the}\mathrm{string}\mathrm{with}\mathrm{vertical},\theta =45° \\ \mathrm{Tension}\mathrm{of}\mathrm{the}\mathrm{string}\left(T\right)\mathrm{is}\mathrm{given}\mathrm{by} \\ T=\frac{m{v}^2}{r}+mg\cos \theta \\ \Rightarrow T=\frac{0.5\times {\left(3\right)}^2}{1.5}+0.5\times 9.8\times \frac{1}{\sqrt{2}} \\ \Rightarrow T=3+3.47=6.47\mathrm{N} \end{gathered}$$