The force exerted by a compression device is given by F(x)=kx(x−l) for 0≤x≤l, where l is the maximum possible compression, x is the compression and k is the constant. Work done to compress the device by a distance d will be maximum when
d=l4
d=l√2
d=l2
d=l
A
d=l2
B
d=l
C
d=l√2
D
d=l4
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Solution
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For W to be maximum ; dWdx=0;
i.e. F(x)=0⇒x=l,x=0
clearly for d=l, the work done is maximum.
Alternate Solution : External force and displacement are in the same direction ∴ Work will be positive continuously so it will be maximum when displacement is maximum.
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