Given below are two statements : One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : Product of Pressure (P) and time (t) has the same dimension as that of coefficient of viscosity.
Reason R : Coefficient of viscosity = Force/(Velocity gradient)
Choose the correct answer from the options given below :

Solution

Physics sir · 3 steps

Write the dimensions of each side, and do not forget the area in Newton's law of viscosity.

1. Correct viscosity law. Newton's law of viscosity is F = η A dv/dx, so η = F/(A (dv/dx)). The force is divided by area and by velocity gradient.

   Quantity	Built from	Dimensions
   P × t	[ML⁻¹T⁻²] × [T]	[ML⁻¹T⁻¹]
   η = F/(A (dv/dx))	[MLT⁻²]/[L²][T⁻¹]	[ML⁻¹T⁻¹]
   F/(dv/dx) (Reason R)	[MLT⁻²]/[T⁻¹]	[MLT⁻¹]

2. Check each statement. P × t matches η exactly, so Assertion A is true. Force divided by velocity gradient gives [MLT⁻¹], which is not the dimension of viscosity, so Reason R is false.
3. So. A is true but R is false, which is option (c).

The idea to keep. Viscosity is force per unit area per unit velocity gradient. Since force per area is pressure, η has the dimensions of pressure times time.

Answer from the NTA final answer key. Solution by PrepWiser.