Question

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

A
30 J
B
15 J
C
25 J
D
20 J

Solution

## The correct option is A 15 J$$W=$$ area under $$F-x$$ graphFrom $$X=0$$ to $$X=1$$, force and displacement both are positive. Therefore work done is positive.$$W_0=+Area=+5J$$From $$X=1$$ to $$X=3$$, force and displacement both are positive. Therefore work done is positive.$$W_1=+Area=+15J$$From $$X=3$$ to $$X=4$$, force is negative but displacement is positive. Therefore work done is again positive.$$\therefore W_2=-Area=-5J$$From $$X=4$$ to $$X=5$$, force and displacement both are positive. Therefore work done is again positive.$$\therefore W_3=+Area=+5J$$$$W_{Total}=W_0 +W_1+W_2+W_3=20J$$Physics

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