question_answer 55)

                  A body of mass l0kg is acted upon by two perpendicular forces, 6N and 8N. The resultant acceleration of the body is                 (a) \[1\text{ }m\text{ }{{s}^{2}}\] at an angle of \[{{\tan }^{1}}\left( \frac{4}{3} \right)\] w.r.t. 6 N force.                 (b) \[0.2\text{ }m\text{ }{{s}^{-2}}\] at an angle of \[{{\tan }^{1}}\left( \frac{4}{3} \right)\] w.r.t. r. 6 N force.                 (c) \[1\text{ }m{{\text{s}}^{-2}}\] at an angle of \[{{\tan }^{-1}}\left( \frac{3}{4} \right)\] w.r.t. 8 N force.                 (d) \[0.2\text{ }m{{s}^{2}}\] at an angle of \[{{\tan }^{1}}\left( \frac{3}{4} \right)\] w.r.t 8 N force.

Answer:

                  (a, c) Ist case: Net force, \[F=\sqrt{F_{1}^{2}+F_{2}^{2}}\]                 \[=\,\sqrt{36+64}\,=\,10\,N.\,\]                 \[\therefore \] \[a=\,\frac{F}{m}\,=\,\frac{10}{10}\,=1\,m{{s}^{-2}}\]                 \[\tan \,\theta \,=\,\frac{8}{6}=\,\frac{4}{3}\] or \[\theta \,=\,{{\tan }^{-1}}\,\left( \frac{4}{3} \right)\]                 2nd case: \[a=1\text{ }m{{s}^{2}}\]                 and \[\tan \,\theta =\frac{6}{8}\,=\,\frac{3}{4}\]                 or \[\theta =\,{{\tan }^{-1}}\left( \frac{3}{4} \right)\]