For which of the following physical quantities is the SI unit not the pascal?

Introduction / Context:
In mechanics and material science, many different physical quantities are measured with SI units that may look similar. Pressure, stress and various elastic moduli are closely related, and all of them involve force over area. The pascal is the SI unit that appears repeatedly in this group. However, not every mechanical quantity uses the pascal, and competitive exams often ask you to pick the one that does not fit.

Given Data / Assumptions:
• The pascal is defined as one newton per square metre, written as N/m^2.
• The question lists several quantities: moment of inertia, pressure, stress, Young modulus and bulk modulus.
• We must identify which quantity does not use the pascal as its SI unit.

Concept / Approach:
Pressure is force per unit area, so its SI unit is N/m^2, which is the pascal. Stress is also defined as internal force per unit area within a material, so it has the same SI unit, the pascal. Young modulus and bulk modulus describe ratios of stress to strain. Since strain is dimensionless, the units of these moduli are identical to the units of stress, again pascal. Moment of inertia is completely different. It involves mass multiplied by the square of distance and is measured in kilogram metre squared.

Step-by-Step Solution:
Step 1: Recall that pressure = force / area, so its unit is newton per square metre, that is the pascal. Step 2: Recall that stress is internal force / area, so its unit is also newton per square metre, the pascal. Step 3: Recall that Young modulus = stress / strain, and since strain has no units, Young modulus has the same unit as stress, the pascal. Step 4: Bulk modulus is also a ratio of stress to fractional volume change, so again its unit is the pascal. Step 5: Moment of inertia depends on mass and length squared and has SI unit kilogram metre squared, not pascal, so this is the correct choice.

Verification / Alternative check:
You can verify quickly by dimensional analysis. Force has dimensions of mass times acceleration, so M L T^-2. Area has dimensions L^2. Pressure therefore has dimensions M L^-1 T^-2. The same dimensions apply to stress and all elastic moduli derived from it. In contrast, moment of inertia is defined as the sum or integral of m * r^2, so it has dimensions M L^2. Because these dimensional patterns are completely different, their SI units must also be different. This confirms that moment of inertia is the odd one out.

Why Other Options Are Wrong:
Pressure: By definition force per unit area, so its unit is N/m^2, which is exactly one pascal.
Stress: Internal force per unit area inside a body, same unit N/m^2, so also measured in pascal.
Young modulus: Ratio of stress to strain, strain has no units, so Young modulus has the same unit as stress, that is the pascal.
Bulk modulus: Also a stress based modulus, defined as pressure change divided by fractional volume change, and therefore it has unit pascal.

Common Pitfalls:
A frequent error is to think that because a modulus sounds like a different type of quantity, it must have some special unit. In fact, whenever you divide a quantity with units by a dimensionless quantity, the units remain unchanged. Therefore all stress based moduli share the pascal as their SI unit. Another mistake is confusing moment of inertia with mass or weight. Remember that moment of inertia always involves a distance squared factor, which immediately distinguishes its unit as kilogram metre squared.

Final Answer:
Moment of inertia is not measured in pascal; its SI unit is kilogram metre squared, whereas pressure, stress and the elastic moduli all use the pascal.