સ્થિર સ્થિતિમાં રહેલ ન્યુક્લિયસનું સમાન ઘનતાવાળા અને 1 : 2ના પ્રમાણમાંની ત્રિજ્યા ધરાવતાં બે ન્યુક્લિયસમાં વિભાજન થાય છે, તો તેમના વેગનો ગુણોત્તર___________થાય.

A 2:1
B 4:1
C 6:1
D 8:1

Verified Solution

Answer & Solution

Correct Answer

(D) 8:1

Step-by-step Solution

Detailed explanation

D
વેગમાન સરંક્ષણના નિયમ પરથી
\(M_1 v_1=M_2 v_2\)
\(\begin{aligned} & \therefore\left(9 \frac{4}{3} \pi r_1^3\right) v_1=\left(9 \frac{4}{3} \pi r_2^3\right) v_2 \\ & \therefore r_1^3 v_1=r_2^3 v_2 \\ & \therefore \frac{v_1}{v_2}=\left(\frac{r_2}{r_1}\right)^3 \\ & \therefore \frac{v_1}{v_2}=\left(\frac{2}{1}\right)^3\left(\because \frac{r_1}{r_2}=\frac{1}{2}\right) \\ & \therefore \frac{v_1}{v_2}=\frac{8}{1}\end{aligned}\)

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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