Question

A plane is in level fight at constant speed and each of its two wings has an area of $234 \mathrm {~km} \mathrm {~h} ^ { - 1 }$ respectively, then the mass of the plane is

(Take the density of the air = 1 kg)

• A. 1550 kg
• B. 1750 kg
• C. 3500 kg
• D. 3200 kg

Answer 1

Answer: (C)

3500 kg

Answer 2

Let $\mathrm { P } _ { 1 }$ and are the pressure there

According to Bernoulli’s theorem

Here,

$\mathrm { v } _ { 2 } = 270 \mathrm {~km} \mathrm {~h} ^ { - 1 } = 270 \times \frac { 5 } { 18 } = 75 \mathrm {~ms} ^ { - 1 }$

Area of wings $= 2 \times 25 \mathrm {~m} ^ { 2 } = 50 \mathrm {~m} ^ { 2 }$

$\therefore \mathrm { P } _ { 1 } - \mathrm { P } _ { 2 } = \frac { 1 } { 2 } \times 1 \left( 75 ^ { 2 } - 65 ^ { 2 } \right)$

Upward force on the plane

$= \left( \mathrm { P } _ { 1 } - \mathrm { P } _ { 2 } \right) \mathrm { A }$

$= \frac { 1 } { 2 } \times 1 \times \left( 75 ^ { 2 } - 65 ^ { 2 } \right) \times 50 \mathrm {~m}$

As the plane is in level flight therefore upward force balances the weight of the plane.

$\therefore \mathrm { mg } = \left( \mathrm { P } _ { 1 } - \mathrm { P } _ { 2 } \right) \mathrm { A }$

Mass of the plane,

$= \frac { 1 } { 2 } \times \frac { 1 \times \left( 75 ^ { 2 } - 65 ^ { 2 } \right) } { 10 } \times 50$

$= \frac { ( 75 + 65 ) ( 75 - 65 ) \times 50 } { 2 \times 10 }$

$= 3500 \mathrm {~kg}$