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) \[\left( \frac{14Vg\sigma +w}{Vg\sigma -w} \right)\times g\]
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\[=V15\sigma g-(Vg\sigma \times w)\] \[or\,\,a=\left( \frac{14Vg\sigma -w}{Vg\sigma +w} \right)\times g\]
You need to login to perform this action.
You will be redirected in
3 sec
