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Question

# Look at the activity listed here. Reason out whether or not work is done in the light of your understanding of the term 'work'. Suma is swimming in a pond.

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Solution

## Work doneWork done is defined as the force applied to displace a body from its original state.Force and displacement are vector quantities.We know that the dot product of two vectors gives a scalar quantity as its result.Thus, work done is a scalar quantity. If $\stackrel{\to }{F}$ is the force applied and $\stackrel{\to }{S}$ is the displacement of the body, then the work done $W$ can be given as, $W=\stackrel{\to }{F}.\stackrel{\to }{S}$ $=FS\mathrm{cos}\theta$, where, $\theta$ is the angle between the direction of the force vector and displacement vector.Finding whether work is done or notIn order to swim a force needs to be applied by the hand inside the water, to push the water backward.This causes the water to exert a reaction force on Suma and she can move forward. $\therefore \theta =180°$ $=FS\mathrm{cos}180°=-FS$Hence, the work done is negative.

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