Question

Which of the following statements is correct regarding the work done $\overrightarrow{F}$ along these two paths.

• A. Work done on x-axis is zero
• B. Work done on x-axis is less than on y-axis
• C. Work done on x-axis is more than on y-axis but not zero
• D. Data insufficient

Answer 1

The correct option is A Work done on x-axis is zero

since force is applied in -ve y-axis and angle between x & y axis is ${90}^o$
and $dW=\overrightarrow{F}\cdot \overrightarrow{ds}$
$W=0$ on x-axis
Alternatively, since $y=0$ along the path from $x=0$( origin) to $x=3$, $\overrightarrow{F}=\alpha x{y}^2\hat{j}=0$ $\Rightarrow W=\overrightarrow{F}\cdot \overrightarrow{ds}=0$
Similarly, $W=0$ along y-axis.