Inspired by Dish-washing!

Consider the following diagram-

L is a murky ideal liquid of refractive index \(n=2.23\) filled in a container C of cross section Z to a height of H= 64cm. Container C has an orifice O (near the bottom) of cross section z from which the liquid flows out starting at a time t = 0. L has a unique property that the intensity of light transmitted through it varies as \(I=I_{initial}e^{-10d}\) where d is the distance travelled by light through the the liquid.The bottom R of C is reflecting (perfectly). A (of mass 50g) consists of a floating light emitter (it emits a narrow beam of light) a and receiver b which lie very close to each other. a emits light of intensity \(I_{0}\) and \(b\) responds only when it receives light of intensity greater than \(0.04076I_{0}\). If t(to the nearest positive integer) is the time after which b responds and if U is the loss in potential energy of A in the time interval between the emission of the light ray which produces the first response and the reception of the same such that \(U=m10^{-x}\),

find |t| + x.

Given: - \(\frac{z}{Z} =10^{-4}\)

  • \(c= 3 \times 10^{8}ms^{-1}\)

  • \(g= 10ms^{-2}\)


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