Question

A force $F$ acting on an object varies with distance $x$ as shown in the figure.
The work done by the force in moving the object from $x=0$ and $x=8m$ is

• A. $ZeroJ$
• B. $80J$
• C. $-40J$
• D. $40J$

Answer 1

Answer: (A)

$ZeroJ$

From the given graph

Relation between $F$ and $x$ is given by:-

$F=20-5x$

The work done by the force in moving the object from $x=0$ and $x=8$ m is, $W={\int }_0^{8}F\cdot dx$

$⟹W={\int }_0^8(20-5x)\cdot dx$

$⟹W=[20x-\frac{5}{2}{x}^2{]}_0^8=160-160=0$

Hence, option $\left(A\right)$ is correct