Question 107: Units , Dimensions and Error Analysis

Question

Match List I with List II

LIST I

LIST II

A.
Torque
I.
$$\mathrm{ML^{-2}T^{-2}}$$

B.
Stress
II.
$$\mathrm{ML^2T^{-2}}$$

C.
Pressure gradient
III.
$$\mathrm{ML^{-1}T^{-1}}$$

D.
Coefficient of viscosity
IV.
$$\mathrm{ML^{-1}T^{-2}}$$

Choose the correct answer from the options given below:

Accepted Answer

Let's analyze the SI units of each quantity from List I:
Torque: Torque (ÃÂ) is given by the cross product of the radius (r) and the force (F). Therefore, its SI units are Newton meter (Nm), which translates to $$\mathrm{ML^2T^{-2}}$$ in fundamental units.
Stress: Stress is force per unit area. The SI unit for force is the Newton (N) and for area is meter squared (mÃÂ²). Therefore, the SI unit for stress is Pascal (Pa), which translates to $$\mathrm{ML^{-1}T^{-2}}$$ in fundamental units.
Pressure gradient: The pressure gradient is the rate of increase or decrease in pressure. It has units of pressure per distance. In SI units, that's Pascal per meter (Pa/m), which translates to $$\mathrm{ML^{-2}T^{-2}}$$ in fundamental units.
Coefficient of viscosity: This is a measure of a fluid's resistance to shear or flow, and its SI units are the Pascal second (Pa.s), which translates to $$\mathrm{ML^{-1}T^{-1}}$$ in fundamental units.
Therefore, the correct matches are:
A - II
B - IV
C - I
D - III

Answer

A-II, B-I, C-IV, D-III

Answer

A-II, B-IV, C-I, D-III

Answer

A-IV, B-II, C-III, D-I

Answer

A-III, B-IV, C-I, D-II

Units , Dimensions and Error Analysis

Match List I with List II LIST I LIST II A. Torque I. $\mathrm{ML^{-2}T^{-2}} B. Stress II. \mathrm{ML^2T^{-2}} C. Pressure gradient III. \mathrm{ML^{-1}T^{-1}} D. Coefficient of viscosity IV. \mathrm{ML^{-1}T^{-2}}$ Choose the correct answer from the options given below:

Choose the correct answer: