Water enters a container at a rate proportional to the square of the amount present. Starting from volume V 0 , it reaches 2 V 0 in 6 hours. How many hours from the start until it reaches 4 V 0

Question

Water enters a container at a rate proportional to the square of the amount present. Starting from volume V 0 ​ , it reaches 2 V 0 ​ in 6 hours. How many hours from the start until it reaches 4 V 0 ​ ?

TestHub · Accepted Answer

d V / d t = k V 2 gives 1/ V = 1/ V 0 ​ − k t . The 2 V 0 ​ condition gives k = 1/ ( 12 V 0 ​ ) . Setting V = 4 V 0 ​ yields t = 9 hours.

Mathematics - Application of Derivative Question with Solution | TestHub

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JEE Advanced 2027 (Class 12+)