The relation between the displacement $X$ of an object produced by the application of the variable force $F$ is represented by a graph shown in the figure. If the object undergoes a displacement from $X = 0.5\,m$ to $X = 2.5\,m$ the work done will be approximately equal to .............. $J$
The relation between the displacement $X$ of an object produced by the application of the variable force $F$ is represented by a graph shown in the figure. If the object undergoes a displacement from $X = 0.5\,m$ to $X = 2.5\,m$ the work done will be approximately equal to .............. $J$
$16 $
$32$
$1.6$
$8 $
The relation between the displacement $X$ of an object produced by the application of the variable force $F$ is represented by a graph shown in the figure. If the object undergoes a displacement from $X = 0.5\,m$ to $X = 2.5\,m$ the work done will be approximately equal to .............. $J$
Work done = Area under curve and displacement axis
= Area of trapezium
= $\frac{1}{2}$ $×$ (sum of two parallel lines) $×$ distance between them
= $\frac{1}{2}(10 + 4) \times (2.5 - 0.5)$
= $\frac{1}{2}14 \times 2$ $= 14 \,J$
As the area actually is not trapezium so work done will be more than $14 J$ i.e. approximately $16\, J$