| A pipe of diameter d can drain a certain water tank in 40 min. The time taken by a pipe of diameter 2d for doing the same job in |
A) 5 min
B) 10 min
C) 20 min
D) 80 min
Correct Answer: B
Solution :
| Given, \[{{t}_{1}}=40,\]\[{{d}_{1}}=d,\]\[{{d}_{2}}=2d\] |
| Time \[\propto \frac{1}{\text{Cross}\,\,\text{section}\,\,\text{area}\,\,\text{of}\,\,\text{pipe}}\] |
| \[\Rightarrow \] \[{{t}_{1}}\propto \frac{1}{\frac{\pi }{4}d_{1}^{2}}\]and \[{{t}_{2}}\propto \frac{1}{\frac{\pi }{4}d_{2}^{2}}\] |
| \[\Rightarrow \] \[\frac{{{t}_{2}}}{{{t}_{1}}}={{\left( \frac{{{d}_{1}}}{{{d}_{2}}} \right)}^{2}}\] |
| \[\therefore \] \[{{t}_{2}}=40{{\left( \frac{d}{2d} \right)}^{2}}=10\min \] |
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