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JIPMER 2013

Exam: JIPMER
Year: 2013
Subject: Physics
Chapter: Mechanical Properties of Fluids

JIPMER 2013 · Physics · Mechanical Properties of Fluids

The speed of air flow on the upper and lower surfaces of a wing of...

The speed of air flow on the upper and lower surfaces of a wing of an aeroplane are

v_1

and

v_2

respectively. If

A

is the cross section area of the wing and

\rho

is the density of air, then the upward life is

Options

A $\frac{1}{2} \rho A\left(v_2-v_1\right)$
B $\frac{1}{2} \rho A\left(v_1+v_2\right)$
C $\frac{1}{2} \rho A\left(v_1^2-v_2^2\right)$
D $\frac{1}{2} \rho A\left(v_1^2+v_2^2\right)$

Correct answer

C. $\frac{1}{2} \rho A\left(v_1^2-v_2^2\right)$

Step-by-step solution

(

\begin{aligned} E_{\text{rotational }} & \left.=\frac{1}{2} \right\rvert\, \omega^2 \\ & =\frac{\mathrm{L}^2}{2 \mid} \quad(\because \mathrm{L}=\mid \omega) \end{aligned}

) Therefore, (\mathrm{L}^2=2 \mathrm{EI}) Hence

L_A^2=2 E_A I_A

...(i) and

L_B^2=2 E_B I_B

...(ii) From equation (i) and (ii) (

\begin{aligned} \frac{L_A}{L_B} & =\sqrt{\frac{2 E_A I_A}{2 E_B I_B}} \\ & =\sqrt{\frac{100}{4}} \\ \frac{L_A}{L_B} & =5 \\ \left(\because \frac{E_B}{E_A}\right. & \left.=100 \text{ and } \frac{I_A}{I_B}=4\right) \end{aligned}

)

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