question_answer

Given below is a graph between a variable force (F) (along y-axis) and the displacement (x) (along x-axis) of a particle in one dimension. The work done by the force in the displacement interval between 0 m and 30 m is

A)  275 J                                    

B)  375 J

C)  400 J                                    

D)  300 J

Correct Answer: B

Solution :

                 Work done = area of F-t graph with x-axis Total area = area of\[\Delta ABC\] \[+\text{ }area\text{ }of\text{ }\square BCDE+area\text{ }of\text{ }\square EIJG\]       \[+\,area\,of\,\Delta FGH\] Area of \[\Delta ABC=\frac{1}{2}\times 5\times 10=25\,J\] Area of \[\square BCDE=10\times 10=100\text{ }J\] Area of \[\square EIJG=5\times 30=150\text{ }J\] Area of\[\Delta FGH=\frac{1}{2}\times 10\times 20=100\text{ }J\] \[\therefore \]Total area\[=25+100+150+100=375\text{ }J\]