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Work Done When Force Is Varying

A block is co...

Question

A block is constrained to move along x-axis under a force F=-2x. Here, F is in newton and x in metre. Find the work done by this force when the block is displaced from x=2 m to x=-4 m.

A

-4 J

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B

-8 J

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C

-12 J

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D

-16 J

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Solution

The correct option is B -12 J
Work done by a body in moving an object from $x_{1}$ to $x_{2}$
$= \int_{x_{1}}^{x_{2}} F d x$
$= \int_{x_{1}}^{x_{2}} (- 2 x) d x$
$= x_{1}^{2} - x_{2}^{2}$
$= - 12 J$

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