JEE Advance - Mathematics (2001 - No. 7)
A hemispherical tank of radius $$2$$ metres is initially full of water and has an outlet of $$12$$ cm2 cross-sectional area at the bottom. The outlet is opened at some instant. The flow through the outlet is according to the law $$v(t)=0.6$$ $$\sqrt {2gh\left( t \right),} $$ where $$v(t)$$ and $$h(t)$$ are respectively the velocity of the flow through the outlet and the height of water level above the outlet at time $$t,$$ and $$g$$ is the acceleration due to gravity. Find the time it takes to empty the tank. (Hint: From a differential equation by relasing the decreases of water level to the outflow).
${{14\pi } \over {27\sqrt g }}{\left( {10} \right)^5}
${{7\pi } \over {27\sqrt g }}{\left( {10} \right)^5}
${{14\pi } \over {9\sqrt g }}{\left( {10} \right)^5}
${{14\pi } \over {27\sqrt g }}{\left( {10} \right)^4}
${{14\pi } \over {27\sqrt g }}{\left( {10} \right)^6}