A plane is in level fight at constant speed and each of its two wings has an area of $$25$$ $$m2$$. If the speed of the air on the upper and lower surfaces of the wing are $$270$$ kmph and $$234$$ kmph respectively,then mass of the plane is $$(take$$ the density of air is $$1$$ $$kgm3$$

Question

A plane is in level fight at constant speed and each of its two wings has an area of $$25$$ $$m2$$. If the speed of the air on the upper and lower surfaces of the wing are $$270$$ kmph and $$234$$ kmph respectively,then mass of the plane is $$(take$$ the density of air is $$1$$ $$kgm3$$

Infinity Learn · Accepted Answer

Let $$v1$$, $$v2$$ are the speed of air on the lower and upper surface S of the wings of the plane $$P1$$ and $$P2$$ are the Pressure there.According to Bernoulli's $$theoremP1+12$$ρ$$v12$$ $$=$$ $$P2+12$$ρ$$v22P1-P2$$ $$=$$ $$12$$ρ(v22-v12)Here$$, $$v1$$ $$=$$ $$234$$ km $$h-1$$ $$=$$ $$234$$×$$518ms-1$$ $$=$$ $$65$$ $$ms-1$$ $$v2$$ $$=$$ $$270$$ km $$h-1$$ $$=$$ $$270$$×$$518$$ $$=$$ $$75$$ $$ms-1Area$$ of wings $$=$$ $$2$$× $$25$$ $$m2$$ $$=$$ $$50$$ $$m2P1-P2$$ $$=12$$×$$1(752-652)Upward$$ force on the plane $$=$$ $$(P1-P2)A$$ $$=$$ $$12$$×$$1$$×$$(752-652)×$$50$$ mAs the plane is in level flight, therefore upward force balances the weight of the planemg $$=$$ (P1-P2)AMass$$ of the plane,m $$=$$ $$(P1-P2)gA$$  $$=$$ $$12$$×$$1$$×$$(752-652)10$$×$$50=$$ $$(75+65)(75-65)×$$502$$×$$10$$ $$=$$ $$3500$$ kg

A plane is in level fight at constant speed and each of its two wings has an area of 25 m2. If the speed of the air on the upper and lower surfaces of the wing are 270 kmph and 234 kmph respectively,then mass of the plane is (take the density of air is 1 kgm3

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