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# A particular force acting on object has equation $F=-cx^3$ where x is displacement of object from some orgin and $c=1N/m^3$ What is magnitude of the work done by this force, as the object moves from $x=-2m,\; to\;x=+2m$

$(a)\;16\;J \quad (b)\;8\;J \quad (c)\; 4\;J \quad (d)\;0\;J$

$\int dW=\int F dx$
$\qquad=-c \int \limits_{-2}^2 x^3 dx$
$\qquad=\large\frac{-1}{4}$$\bigg[2^4-(-2)^4\bigg]$
$\qquad=0\;J$
Hence d is the correct answer.

edited Feb 17, 2014 by meena.p

–1 vote