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Question: A particle moves under the effect of a force F = Cx from x = 0 to x = x<sub>1</sub>. The work done i...

A particle moves under the effect of a force F = Cx from x = 0 to x = x1. The work done in the process is

A

Cx12C x _ { 1 } ^ { 2 }

B

12Cx12\frac { 1 } { 2 } C x _ { 1 } ^ { 2 }

C

Cx1C x _ { 1 }

D

Zero

Answer

12Cx12\frac { 1 } { 2 } C x _ { 1 } ^ { 2 }

Explanation

Solution

Work done

=∫x1x2Fdx=∫0x1Cxdx=C[x22]0x1=12Cx12= \int _ { x _ { 1 } } ^ { x _ { 2 } } F d x = \int _ { 0 } ^ { x _ { 1 } } C x d x = C \left[ \frac { x ^ { 2 } } { 2 } \right] _ { 0 } ^ { x _ { 1 } } = \frac { 1 } { 2 } C x _ { 1 } ^ { 2 }