Question

The force exerted by a compression device is given by F(x)=kx (x-l) for 0 less then equal x less then equal l is the maximum
possible compression, x is the compression and k is a constant. The work required to compress
the device by a distance d will be maximum when :
(D) d = l
(A) d =l/4
(B) d=l/√2
(C) d = l/2
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Answer 1

Answer:

(D) d = l

Explanation:

given that

F(x)=k x (x-l)

We know that

work ,w = ∫F.dx

For maximum work

dw/dx = 0

dw/dx = F

So F= 0

F(x)=k x (x-l)

F(x)=k x (x-l) = 0

x- l =0

x=l

it means that at distance d=l then work will be maximum.

(D) d = l