GATE 2026 BT Q.45: solution and answer

Official answer: DSource: Official answer key, GATE 2026 BT (IIT Guwahati)

1. A Newtonian fluid obeys Newton's law of viscosity: $\tau =\mu \dot{\gamma }$, where $\tau$ is the shear stress, $\dot{\gamma }$ is the shear rate and $\mu$ is the viscosity.

2. With $\tau$ on the Y axis and $\dot{\gamma }$ on the X axis this reads $y=\mu x$. This is a straight line through the origin with slope $\mu$.

3. For a Newtonian fluid $\mu$ is constant and does not change with shear rate, so the plot is a straight line.

4. Viscosity is always positive ($\mu >0$), so the slope is positive. (D) is correct.

5. (A) A line parallel to the X axis has zero slope. That means the stress stays the same whatever the shear rate, so the viscosity would be zero. This is not Newtonian behaviour. Wrong.

6. (B) A line parallel to the Y axis has infinite slope, which means infinite viscosity. That describes a rigid solid, not a fluid. Wrong.

7. (C) A negative slope would mean a negative viscosity, which is physically impossible. Wrong.