Question

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

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

$W=\int \overline{F}.\overline{d}s={\int }_2^1\left(4x\right)dx=[2x^2{]}_2^1=-6J$

Here $\overline{F}$ and $\overline{d}x$ are in opposite direction thus -ve work.

Here force is always in one direction while displacement is always opposite to it.