Fluid Mechanics Viscosity Question 275
Question: A balloon of volume F, contains a gas whose density is to that of the air at the earth’s surface as 1:15. If the envelope of the balloon be of weight w but of negligible volume, find the acceleration with which it will begin to ascend.
Options:
A) $ \left( \frac{7Vg\sigma -w}{Vg\sigma +w} \right)\times g $
B) $ \left( \frac{2Vg\sigma -w}{Vg\sigma +w} \right)\times g $
C) $ \left( \frac{14Vg\sigma -w}{Vg\sigma +w} \right)\times g $
D) $ \left( \frac{14Vg\sigma +w}{Vg\sigma -w} \right)\times g $
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Answer:
Correct Answer: C
Solution:
[c] Let a be the density of the gas, then that of the air is $ 15\sigma $ . Then the weight of the balloon = weight of the gas + weight of the envelope $ =Vg\sigma +w $ If f be the required acceleration of the balloon acting vertically upward and then from “mass acceleration=forces acting in the sense of acceleration” we get $ \frac{(Vg\sigma +w)}{g}\times a $ force of buoyance - wt. of the balloon with gas$ =V15\sigma g-(Vg\sigma \times w) $ $ or,,a=\left( \frac{14Vg\sigma -w}{Vg\sigma +w} \right)\times g $
BETA
