Two 10 cm long aluminium rods and five 8 cm long steel rods are at 5°C temperature and are joined together to form a 60 cm long rod. What is the increase in the length of the joined rod when the temperature is raised at 80°C? (Use a coefficient of linear expansion for aluminium= 2.4×10−5K−1 2.4 × 10^{- 5} K^{- 1} and coefficient of linear expansion for Steel =1.2×10−5K−1) = 1.2 × 10^{- 5} K^{- 1} )

Question

Two 10 cm long aluminium rods and five 8 cm long steel rods are at 5°C temperature and are joined together to form a 60 cm long rod. What is the increase in the length of the joined rod when the temperature is raised at 80°C? (Use a coefficient of linear expansion for aluminium= 2.4×10−5K−1 2.4 × 10^{- 5} K^{- 1} and coefficient of linear expansion for Steel  =1.2×10−5K−1) = 1.2 × 10^{- 5} K^{- 1} )

Accepted Answer

ঘ. 0.72 mm

ব্যাখ্যা: অ্যালুমিনিয়ামের মোট দৈর্ঘ্য $L_{Al} = 2 	imes 10	ext{ cm} = 20	ext{ cm}$ এবং স্টিলের মোট দৈর্ঘ্য $L_{steel} = 5 	imes 8	ext{ cm} = 40	ext{ cm}$। তাপমাত্রার পরিবর্তন $\Delta T = 80^\circ	ext{C} - 5^\circ	ext{C} = 75^\circ	ext{C} = 75	ext{ K}$। মোট দৈর্ঘ্যের বৃদ্ধি $\Delta L = \Delta L_{Al} + \Delta L_{steel} = (L_{Al}\alpha_{Al} + L_{steel}\alpha_{steel})\Delta T = (20	imes 2.4	imes 10^{-5} + 40	imes 1.2	imes 10^{-5})	imes 75 = (4.8	imes 10^{-4} + 4.8	imes 10^{-4})	imes 75 = 9.6	imes 10^{-4}	imes 75 = 0.072	ext{ cm} = 0.72	ext{ mm}$।

পদার্থবিজ্ঞান প্রশ্ন

সম্পর্কিত প্রশ্ন