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Work Done, Varying Force and Path

Assertion :A ...

Question

Assertion :A body is moved from $x = 2 m$ to $x = 1 m$ , under a force $F = 4 x N$ , then work done by this force is negative. Reason: Force and displacement are in opposite directions.

Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

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Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

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Assertion is correct but Reason is incorrect

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Assertion is incorrect but Reason is correct

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Solution

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
Work done by a force is given by
$W = F . S$
$W = F S cos θ$
where force is acting along positive x-direction but displacement is in negative x-direction.
$∴ cos θ = - 1$
Which means work done is negative.

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