One afternoon Jamil and his friends were Gissing besides a lake . all on a sudden,Jamil notice that a bubble from the bottom of the lake of transparent water was coming out on the surface of the water.after coming to the surface,the bubble took a large size.size on the bubble of the surface was 5 times and atmosphere pressure was 105Nm−2 10^{5} N m^{- 2} .[density of water,p=1000kgm-3] calculate the depth of the lake.

Question

One afternoon Jamil and his friends were Gissing besides a lake . all on a sudden,Jamil notice that a bubble from the bottom of the lake of transparent water was coming out on the surface of the water.after coming to the surface,the bubble took a large size.size on the bubble of the surface was 5 times and atmosphere pressure was   105Nm−2 10^{5} N m^{- 2} .[density of water,p=1000kgm-3] calculate the depth of the lake.

Accepted Answer

খ. 40.82m

ব্যাখ্যা: বুদবুদটির তাপমাত্রা স্থির ধরে বয়েলের সূত্র প্রয়োগ করা যায়: $P_1 V_1 = P_2 V_2$। এখানে হ্রদের তলদেশে চাপ $P_1 = P_{	ext{atm}} + hho g$ এবং আয়তন $V_1$। পানির উপরিভাগে চাপ $P_2 = P_{	ext{atm}} = 10^5	ext{ N m}^{-2}$ এবং আয়তন $V_2 = 5V_1$। অতএব, $P_{	ext{atm}} + hho g = 5 P_{	ext{atm}} \implies hho g = 4 P_{	ext{atm}}$। সুতরাং, $h = \frac{4 	imes 10^5}{1000 	imes 9.8} \approx 40.82	ext{ m}$।

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