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A plane is in level flight at constant s...

A plane is in level flight at constant speed and each of its two wings has an area of `25 m^(2)` . If the speed of the air on the upper and lower surfaces of the wing are `270 km h^(-1)` and `234 km h^(-1)` respectively, then the mass of the plane is (Take the density of the air `=1 kg m^(-3)`)

A

1550 kg

B

1750 kg

C

3500 kg

D

3200 kg

Text Solution

Verified by Experts

The correct Answer is:
C
(c ) , Let `v_(1),v_(2)` are the speed of air on the lower and upper surface S of the wings of the plane `P_(1)` and `P_(2)` are the pressure there.
According to Bernoulli's theorem
`P_(1)+(1)/(2)rhov_(1)^(2)=P_(2)+(1)/(2)rhov_(2)^(2)`
`P_(1)-P_(2)=(1)/(2)rho(v_(2)^(2)-v_(1)^(2))`
Here, `v_(1)=234" km " h^(-1)=234xx(5)/(18)m s^(-1)=65 ms^(-1)`
`v_(2)=270" km " h^(-1)=270xx(5)/(18)m s^(-1)=75 ms^(-1)`
Area of wing `=2xx25 m^(2)=50 m^(2)`
`:. P_(1)-P_(2)=(1)/(2)xx(75^(2)-65^(2))`
Upward force on the plane `=(P_(1)-P_(2))A`
`=(1)/(2)xx1xx(75^(2)-65^(2))xx50 m`
As the plane is in level flight, therefore upward force balances the weight of the plane.
`:. mg =(P_(1)-P_(2))A`
Mass of the plane,
`m=((P_(1)-P_(2)))/(g)A=(1)/(2)xx(1xx(75^(2)-65^(2)))/(10)xx50`
`=((75+65)(75-65)xx50)/(2xx10)=3500" kg"`
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