question_answer

A body of mass 6 kg is under a force which causes displacement in it given by\[S=\frac{{{t}^{2}}}{4}m\]where 't' is time. The work done by the force in 2 s is (a) 12 J                                  (b) 9 J (c) 6 J                                     (d) 3 J

Answer:

Given, \[m=6kg\]             \[S=\frac{{{t}^{2}}}{4}m\]   \[t=2s\]   \[W=?\] We know, \[W=F\times S=ma\times S\]               ????..(1) \[(\because \,F=ma)\] From the equation, \[S=ut+\frac{1}{2}a{{t}^{2}}\] We get, \[\frac{{{t}^{2}}}{4}=\frac{1}{2}\times a\times {{t}^{2}}\] \[\Rightarrow \] \[{{t}^{2}}=2a{{t}^{2}}\] \[\Rightarrow \] \[a=\frac{1}{2}\] Substituting all the values in equation., (1), we get \[W=6\times \frac{1}{2}\times 1=3J\]     \[\left[ \because S=\frac{{{t}^{2}}}{4}=\frac{{{2}^{2}}}{4}=1m \right]\]