સાપેક્ષ ઘનતા \(\sigma\) અને વ્યાસ \(D\) ધરાવતા એક ગોળામાં \(d\) વ્યાસનું સમકેન્દ્રીય પોલાણ છે. જો તે પાણી ભરેલી ટાંકીમાં ફક્ત તરે છે, તો \(\frac{D}{d}\) નો ગુણોત્તર _______ છે.

A \(\left(\frac{\sigma}{\sigma-1}\right)^{\frac{1}{3}}\)
B \(\left(\frac{\sigma+1}{\sigma-1}\right)^{\frac{1}{3}}\)
C \(\left(\frac{\sigma+1}{\sigma-1}\right)^{\frac{1}{3}}\)
D \(\left(\frac{\sigma-2}{\sigma+2}\right)^{\frac{1}{3}}\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(\left(\frac{\sigma}{\sigma-1}\right)^{\frac{1}{3}}\)

Step-by-step Solution

Detailed explanation

વજન (w) \(=\frac{4}{3} \pi\left(\frac{D^3-d^3}{8}\right) \sigma g\) ઉત્પ્લાવક બળ \(\left(F_b\right)=1 \times \frac{4}{3} \pi\left(\frac{D^3}{8}\right) \cdot g\) ફક્ત તરવા માટે \(\Rightarrow \mathrm{W}=\mathrm{F}_{\mathrm{b}}\)…

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.

Same subject

સૂચિ-I ને સૂચિ-II સાથે જોડો.

સૂચિ-I	સૂચિ-II
(A) સમતાપી	(I) \(\Delta W(\text{થયેલું કાર્ય}) = 0\)
(B) સમમોષ્મી	(II) \(\Delta Q(\text{supplied heat}) = 0\)
(C) સમદાબ	(III) \(\Delta U(\text{change in internal energy}) \neq 0\)
(D) સમકદ	(IV) \(\Delta U = 0\)

નીચે આપેલા વિકલ્પોમાંથી સાચો ઉત્તર પસંદ કરો :

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