GATE 2026 AE – Question 50
An object of mass 1 kg is launched with an initial speed of $v_o$ into a large tank filled with a viscous liquid. The liquid exerts a resistive force (drag) of the form $D = \alpha v$ on any object that is moving inside it, where $v$ is the instantaneous speed of the object and $\alpha = 1$ kg/s. If the effect of gravity is ignored, the time taken by the object to slow down to the speed $v_o/2$ is ________ s (rounded off to 2 decimal places).
Assume that the tank is sufficiently large for the above deceleration to happen inside the tank.
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Show answer and explanation
Correct answer: 0.68 to 0.70
Explanation
Newton's law gives $m\frac{dv}{dt} = -\alpha v$, so $v = v_o e^{-\alpha t/m} = v_o e^{-t}$. Setting $v = v_o/2$ gives $t = \ln 2 = 0.69$ s.