Question

The force exerted by a compression device is given by $F\left(x\right)=kx(x-l)$ for $0\le x\le l$, 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

• A. $d=\frac{l}{4}$
• B. $d=\frac{l}{\sqrt{2}}$
• C. $d=\frac{l}{2}$
• D. $d=l$

Answer 1

Answer: (D)

For W to be maximum ; $\frac{dW}{dx}=0$;

i.e. $F\left(x\right)=0\Rightarrow x=l,x=0$

clearly for $d=l$, the work done is maximum.

Alternate Solution :
External force and displacement are in the same direction
$\therefore$ Work will be positive continuously so it will be maximum when displacement is maximum.