કોઈ \(m\) દળના કણ પર પ્રયોગમુલક નિયમ પ્રમાણે બળ \(F = \frac{R}{{{t^2}}}\,v(t)\) લગાવવામાં આવે છે. ગતિની શરુઆતની સ્થિર સ્થિતિ થી પ્રાયોગિક રીતે આ નિયમ ની કસોટી કરવી હોય તો તેના માટે ..... નો વક્ર દોરવો એ ઉત્તમ રસ્તો છે.

A \(log\, v(t)\) વિરુદ્ધ \(\frac{1}{t}\)
B \(v(t)\) વિરુદ્ધ \(t^2\)
C \(log\, v(t)\) વિરુદ્ધ \(\frac{1}{t^2}\)
D \(v(t)\) વિરુદ્ધ \(t\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(log\, v(t)\) વિરુદ્ધ \(\frac{1}{t}\)

Step-by-step Solution

Detailed explanation

\begin{array}{l} From\,F = \frac{R}{{{t^2}}}v\left( t \right) \Rightarrow m\frac{{dv}}{{dt}} = \frac{R}{{{t^2}}}v\left( t \right)\\ Integrating\,both\,sides\,\int {\frac{{dv}}{v} = \int {\frac{{Rdt}}{{m{t^2}}}} } \\ In\,v = - \frac{R}{{mt}}\\ \therefore \,In\,v\, \propto…

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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