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 \[0\text{ }m\]and \[30\text{ }m\]is

A)  \[275\text{ }J\]          

B)  \[375\text{ }J\]

C)  \[400\text{ }J\]           

D)  \[300\text{ }J\]

Correct Answer: B

Solution :

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