Question

The force $F$ and position $x$ of a body relates as shown in figure. What will the work done in displacing the body from $x=1m$ to $x=5m$ be ?

• A. $30J$
• B. $15J$
• C. $25J$
• D. $20J$

Answer 1

Answer: (B)

$work$ done equal to area under $F-x$ graph.

Since $work$ is a scalar quantity, so when $area$ is positive $work$ is also positive and vice versa.
So
$W$ $=$ area of rectangle $abce$ $+$ area of rectangle $-$ area of rectangle $ghij+$ area of triangle $jkl$
$W=\left(2-1\right)\times \left(10-0\right)+\left(3-2\right)\times \left(5-0\right)-\left(4-3\right)\times \left(5-0\right)+\frac{1}{2}\times \left(5-4\right)\times \left(10-0\right)\Rightarrow W=1\times 10+1\times 5-1\times 5+\frac{1}{2}\times 1\times 10\Rightarrow W=10+5-5+5\Rightarrow W=15J$