131. (2019). Stol ustidagi ikkita bir xil silindrsimon idishlarga suv quyilgan. Birinchi idishdagi suv sathining balandligi 50 cm , ikkinchi idishdagisi $$ h_{2}\left(h_{2}50 \mathrm{~cm} ight) $$. Idishlarni ingichka nay bilan tutashtirganimizda og'irlik kuchi 100 J ish bajardi. Agar idish asosining yuzasi $$ 1 \mathrm{~m}^{2} $$ bo' $$ 1 \mathrm{sa}, h_{2} \mathrm{ni}(\mathrm{cm}) $$ aniqlang.p.pw $$ =1 \mathrm{~g} / \mathrm{cm}^{3}, \mathrm{~g}=10 \mathrm{~m} / \mathrm{s}^{2} $$. $$ \begin{array}{llll} ext { A) } 70 & ext { B) } 90 & ext { C) } 80 & ext { D) } 60\end{array} $$

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131. (2019). Stol ustidagi ikkita bir xil silindrsimon idishlarga suv quyilgan. Birinchi idishdagi suv sathining balandligi 50 cm , ikkinchi idishdagisi $$ h_{2}\left(h_{2}>50 \mathrm{~cm}ight) $$. Idishlarni ingichka nay bilan tutashtirganimizda og'irlik kuchi 100 J ish bajardi. Agar idish asosining yuzasi $$ 1 \mathrm{~m}^{2} $$ bo' $$ 1 \mathrm{sa}, h_{2} \mathrm{ni}(\mathrm{cm}) $$ aniqlang.p.pw $$ =1 \mathrm{~g} / \mathrm{cm}^{3}, \mathrm{~g}=10 \mathrm{~m} / \mathrm{s}^{2} $$. $$ \begin{array}{llll}	ext { A) } 70 & 	ext { B) } 90 & 	ext { C) } 80 & 	ext { D) } 60\end{array} $$

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Berilgan masalani yechib chiqamiz:

**Ma'lumotlar:**
- Birinchi idishdagi suv balandligi, $$ h_1 = 50 $$ cm.
- Ikkinchi idishdagi suv balandligi, $$ h_2 > 50 $$ cm.
- Idishlarning maydoni, $$ S = 1 $$ m².
- Suv zichligi, $$ \rho = 1 $$ g/cm³ $$ = 1000 $$ kg/m³.
- Gravitatsiya o'zgarishi, $$ g = 10 $$ m/s².
- Qilingan ish, $$ W = 100 $$ J.

**Yechish jarayoni:**

1. **Potensial energiyaning o'zgarishi:**
   Ikki idishdagi suvlar bog'langanidan so'ng, suvlar teng balandlikka ega bo'ladilar. Tenge balandlik, $$ h = \frac{h_1 + h_2}{2} $$.

2. **Potensial energiya formulasi:**
   $$
   U = \frac{1}{2} \rho g S h^2
   $$
   
   Dastlabki energiya:
   $$
   U_{\text{initial}} = \frac{1}{2} \rho g S h_1^2 + \frac{1}{2} \rho g S h_2^2
   $$
   
   Yakuniy energiya:
   $$
   U_{\text{final}} = \rho g S \left( \frac{h_1 + h_2}{2} \right)^2
   $$
   
3. **Ish va energiya o'rtasidagi munosabat:**
   $$
   W = U_{\text{initial}} - U_{\text{final}} = 100 \text{ J}
   $$
   
   Hisoblashni davom ettirsak:
   $$
   (h_2 - h_1)^2 = \frac{400}{\rho g S}
   $$
   
   $$
   (h_2 - 50)^2 = \frac{400}{1000 \times 10 \times 1} = 0.04 \text{ m}²
   $$
   
   $$
   h_2 - 50 = \sqrt{0.04} \times 100 \text{ cm/m} = 20 \text{ cm}
   $$
   
   $$
   h_2 = 50 + 20 = 70 \text{ cm}
   $$

**Javob:**
**A) 70**
$$ h_{2} = 70 $$ cm

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