Salam is using a lift to go to his office where the combined weight of the lift is $5 imes 10^6$ gm. The lift is suspended by a wire of 4 cm diameter. What is the maximum acceleration of the lift which can break the wire, where the breaking stress of the wire is $7.96 imes 10^7 ext{N/m}^2$?

Question

Salam is using a lift to go to his office where the combined weight of the lift is $5 	imes 10^6$ gm. The lift is suspended by a wire of 4 cm diameter. What is the maximum acceleration of the lift which can break the wire, where the breaking stress of the wire is $7.96 	imes 10^7 	ext{N/m}^2$?

Accepted Answer

গ. 10.$2 	ext{ms}^{-2}$

ব্যাখ্যা: লিফটের ভর $m = 5 	imes 10^6	ext{ gm} = 5000	ext{ kg}$
তারের ব্যাসার্ধ $r = \frac{4	ext{ cm}}{2} = 2	ext{ cm} = 0.02	ext{ m}$
প্রস্থচ্ছেদের ক্ষেত্রফল $A = \pi r^2 = \pi 	imes (0.02)^2 = 4\pi 	imes 10^{-4}	ext{ m}^2$

তারের সর্বোচ্চ সহ্যক্ষম টান:
$$T_{\max} = 	ext{Stress} 	imes A = (7.96 	imes 10^7) 	imes (4\pi 	imes 10^{-4}) \approx 10^5	ext{ N}$$
লিফটের ঊর্ধ্বমুখী ত্বরণ $a$ হলে:
$$T - mg = ma \implies a = \frac{T}{m} - g = \frac{10^5}{5000} - 9.8 = 20 - 9.8 = 10.2	ext{ ms}^{-2}$$

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