MHT CET · Maths · Differential Equations

A wet substance in the open air loses its moisture at a rate proportional to the moisture content. If a sheet, hung in the open air, loses half its moisture during the first hour, then \(90 \%\) of the moisture will be lost in ...... hours.

A \(2 \log _2 10\)
B \(\frac{4 \log 10}{\log 2}\)
C \(\log _2 10\)
D \(\frac{3 \log 10}{\log 2}\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(\log _2 10\)

Step-by-step Solution

Detailed explanation

\(M(t) = M_0 \left(\frac{1}{2}\right)^t\) \(\frac{1}{2} M_0 = M_0 \left(\frac{1}{2}\right)^1 \Rightarrow \text{This step is for confirmation of the model, not a calculation of a constant.}\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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