Properties Of Solids And Liquids Question 240
Question: When a body falls in air, the resistance of air depends to a great extent on the shape of the body, 3 different shapes are given. Identify the combination of air resistances which truly represents the physical situation. (The cross sectional areas are the same). [KCET 2005]
Options:
A)$ \frac{8}{9}X $
B)$ \frac{9}{8}X $
C)$ \frac{5}{7}X $
D)$ \frac{7}{5}X $
Show Answer
Answer:
Correct Answer: A
Solution:
Fluid resistance is given by $ R=\frac{8\eta l}{\pi r^{4}}. $
When two capillary tubes of same size are joined in parallel, then equivalent fluid resistance is $ R _{e}=R _{1}+R _{2}=\frac{8\eta L}{\pi r^{4}}+\frac{8\eta \times 2L}{\pi {{(2R)}^{4}}}=\left( \frac{8\eta L}{\pi r^{4}} \right)\times \frac{9}{8} $
Equivalent resistance becomes $ \frac{9}{8} $ times so rate of flow will be $ \frac{8}{9}X $
