\(M\) દળ ધરાવતો એક ફુગ્ગો અને તેની અંદરની સામગ્રી ' \(a\) ' પ્રવેગથી ઉપરની દિશામાં ગતિ કરી રહ્યા છે. ફુગ્ગાને ' \(3 a^{\prime}\) પ્રવેગથી ઉપર તરફ ગતિ કરાવવા માટે, તેની સામગ્રીમાંથી કેટલું દળ મુક્ત કરવું પડશે?
( ' g ' ને ગુરુત્વીય પ્રવેગ લો)

A \(\frac{2 \mathrm{Ma}}{3 \mathrm{a}+\mathrm{g}}\)
B \(\frac{3 \mathrm{Ma}}{2 \mathrm{a}-\mathrm{g}}\)
C \(\frac{3 \mathrm{Ma}}{2 \mathrm{a}+\mathrm{g}}\)
D \(\frac{2 \mathrm{Ma}}{3 \mathrm{a}-\mathrm{g}}\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{2 \mathrm{Ma}}{3 \mathrm{a}+\mathrm{g}}\)

Step-by-step Solution

Detailed explanation

\(\begin{aligned} & F-m g=m a \\ & F=m a+m g \\ & F-(m-x) g=(m-x) 3 a \end{aligned}\) Put F \(\begin{aligned} & \mathrm{Ma}+\mathrm{mg}-\mathrm{mg}+\mathrm{xg}=3 \mathrm{ma}-3 \mathrm{xa} \\ & \mathrm{x}=\frac{2 \mathrm{ma}}{\mathrm{~g}+3 \mathrm{a}} \end{aligned}\)

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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