Project ForgeEngineering Mathematics
Differential Equations
GATE 2018
Medium
Initial water level in a tank is 4m. dL/dt=−k√t, k=0.6 m·s^(−3/2). The level (m) at t=0.5s is (rounded off to second decimal place)
3.86 m(± 0.03 accepted)
Explanation
L(t)=4−∫0^t k√t'dt'=4−(2k/3)t^1.5=4−0.4×(0.5)^1.5=4−0.4×0.3536=3.86m.
Source: GATE CH 2018 (2018)
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