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  4. The relationship between the force F and position x of a body is shown in figure. The work done in displacing the body from x = 1 m to x =5 m will be

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Q. The relationship between the force $F$ and position $x$ of a body is shown in figure. The work done in displacing the body from $x = 1\, m$ to $x =5\,m$ will bePhysics Question Image

UPSEEUPSEE 2014

Solution:

Work done $=$ area enclosed by $F-x$ graph.
image
$=$ Area of $O A M+$ Area of $A B N M+$ Area of $C D E N$ $-$ Area of $E F G H+$ Area of $H I J$ $=\frac{1}{2} \times 1 \times 10+1 \times 10+1 \times 5-1 \times 5+\frac{1}{2} \times 1 \times 10$
$=5 + 10 + 5 - 5 + 5 =20\, J$