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MHT CET202312 May 2023Evening ShiftMathematicsApplication of DerivativesActual

Water flows from the base of rectangular tank, of depth 16 meters. The rate of flow of the water is proportional to the square root of depth at any time t . If depth is 4 ~m when t =2 hours, then after 3.5 hours the depth (in meters) is

Options

  1. A0
  2. B0.25
  3. C0.5
  4. D3

Correct answer

B. 0.25

Step-by-step solution

Given that d x dt x d x dt = a x , for real number a d x x = adt 2 x = at + c When t =0, x=16 (i) c =8 (i) becomes 2 x = at +8 When t =2, x=4 (ii) a =-2 (ii) becomes 2 x =-2 t+8 when t =3.5 (iii) x=0.25 ~m

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