Question

An aircraft of mass $500 \mathrm {~m} ^ { 2 }$in level flight at a speed of 720 $= 10 \mathrm {~m} \mathrm {~s} ^ { - 2 }$)

• A. 0.04
• B. 0.08
• C. 0.17
• D. 0.34

Answer 1

Answer: (C)

0.17

Answer 2

The weight of the aircraft is balanced by the upward force due to the pressure difference.

i.e. $\Delta \mathrm { P } \times \mathrm { A } = \mathrm { mg }$

$\Delta \mathrm { P } = \frac { \mathrm { mg } } { \mathrm { A } } = \frac { \left( 4 \times 10 ^ { 5 } \mathrm {~kg} \right) \left( 10 \mathrm {~ms} ^ { - 2 } \right) } { 500 \mathrm {~m} ^ { 2 } } = \frac { 4 } { 5 } \times 10 ^ { 4 } \mathrm { Nm } ^ { - 2 }$

$= 8 \times 10 ^ { 3 } \mathrm { Nm } ^ { - 2 }$

Let $\mathrm { P } _ { 1 } , \mathrm { P } _ { 2 }$ are the pressure there.

Using Bernoulli’s theorem, we get

Or

Here,

$= 720 \times \frac { 5 } { 18 } \mathrm {~ms} ^ { - 1 } = 200 \mathrm {~ms} ^ { - 1 }$

$= \frac { 4 \times 10 ^ { 4 } } { 5 \times 1.2 \times 4 \times 10 ^ { 4 } } = 0.17$