question_answer 48)

                  A body with mass 5 kg is acted upon by a force                 \[\vec{F}\,=(-3\hat{i}\,+\,4\hat{j})\,\,N\]. If its initial velocity at \[t=0\] is \[\vec{\upsilon }=(6\hat{i}-12\hat{j})\,\,m{{s}^{-1}}\], the time at which it will just have a velocity along the y-axis is                 (a) never                             (b) 10 s                 (c) 2 s                                    (d) 15 s

Answer:

                  (b) \[{{F}_{x}}=3N,\text{ }{{F}_{y}}4N\]                 \[{{\upsilon }_{ax}}\,=6\,m{{s}^{-1}},\,\,{{\upsilon }_{ay}}=-12\,m{{s}^{-1}}\]                 Now, \[{{a}_{x}}\,=\frac{{{F}_{x}}}{m}=\,\frac{-3}{5}\,m{{s}^{-2}}\]                 Using \[{{\upsilon }_{x}}\,={{\upsilon }_{ax}}+\,at=6\,-\frac{3}{5}\,t\]                 Since, \[{{\nu }_{x}}\,=0\,\,\therefore \,\frac{3}{5}\,t\,\,=6\] or \[t=10s\,\,\]