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Chapter 1: Problem 144

Which physical quantity has unit of pascal - second? (a) Force (b) Energy (c) Coefficient of viscosity (d) velocity

Short Answer

Expert verified
The physical quantity with the unit of Pascal-second (Pa·s) is the Coefficient of Viscosity. The correct answer is option (c).

Step by step solution

01

Analyze Option (a) - Force

Force is measured in Newtons (N), which is equal to kg·m/s². Here, we can see that the unit of Force does not include Pascal or seconds. So, option (a) is not the correct answer.
02

Analyze Option (b) - Energy

Energy is measured in Joules (J), which is equal to N·m or kg·m²/s². Here, we can see that the unit of Energy also does not include Pascal or seconds. So, option (b) is not the correct answer.
03

Analyze Option (c) - Coefficient of viscosity

Coefficient of viscosity (η) is a measure of a fluid's resistance to flow. Its unit is given by: η = \( \frac{Force \times Time}{Area} \) The unit of force is Newton (N) and the unit of area is m². Thus the unit of coefficient of viscosity becomes \( \frac{N \cdot s}{m^2} \) Now, we know that 1 Pascal (Pa) is equal to \( \frac{N}{m^2} \), so we can rewrite the unit of coefficient of viscosity as: \( \frac{Pa \cdot N \cdot s}{N} \) Cancelling out the N, we get: \( Pa \cdot s \) Thus, the unit of coefficient of viscosity is Pascal-second (Pa·s). So, option (c) is the correct answer.
04

Analyze Option (d) - Velocity

Velocity is measured in meters per second (m/s). Here, we can see that the unit of Velocity does not include Pascal. So, option (d) is not the correct answer.
05

Conclusion

As shown in Step 3, the physical quantity with the unit of Pascal-second (Pa·s) is the Coefficient of Viscosity. The correct answer is option (c).

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