\(1\,mm\) ત્રિજ્યા અને \(10.5\,g / cc\) ની ધનતા ધરાવતી ગોળીને \(9.8\) પોઈઝ શ્યાનતા ગુણાંક અને \(1.5\,g / cc\) ધનતા ધરાવતા ગ્લિસરીનમાં પડવા દેવામા આવે છે. જયારે ગોળી અચળ વેગ પ્રાપ્ત કરે ત્યારે શ્યાનતાનું બળ \(3696 \times 10^{-x}\,N\) છે.તો \(x\) નું મૂલ્ય કેટલું હશે ? \(( g =9.8\,m / s ^2\) આપેલું છે.)

A \(4\)
B \(5\)
C \(7\)
D \(6\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(7\)

Step-by-step Solution

Detailed explanation

When the ball attain terminal velocity \(F _r=\left( mg - F _{ B }\right)(\because a =0)\) \(= V \sigma_{ b } g - V \rho_{\ell} g\) \(= Vg \left(\sigma_{ b }-\rho_{\ell}\right)\) \(=\frac{4}{3} \pi\left(10^{-3}\right)^3 \times 9.8(10.5-1.5) \times 10^3\)…

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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