Work Energy And Power Question 149
Question: The force exerted by a compression device is given by $ F(x)=kx(x-l)for0\le x\le l $ , where $ l $ is the maximum possible compression, $ x $ is the compression and is a constant. The work required to compress the device by a distance $ d $ will be maximum when:
Options:
A) $ d=\frac{l}{4} $
B) $ d=\frac{l}{\sqrt{2}} $
C) $ d=\frac{l}{2} $
D) $ d=l $
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Answer:
Correct Answer: D
Solution:
[d] For W to be maximum;
$ \frac{dW}{dx}=0 $ ; i.e. $ F(x)=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.
