2- Which of the two have same dimensions(a) Force and strain (b) Force and stress(c) Angular velocity and frequency (d) Energy and strain

To determine which of the given pairs have the same dimensions, let's analyze each option:

(a) Force and strain:

• Force is measured in Newtons (N), which is a unit of mass times acceleration (kg·m/s^2).
• Strain is a dimensionless quantity, as it represents the deformation or change in shape of an object.

Since force is measured in units of mass times acceleration and strain is dimensionless, force and strain do not have the same dimensions.

(b) Force and stress:

• Force is measured in Newtons (N), as mentioned before.
• Stress is measured in Pascals (Pa), which is a unit of force per unit area (N/m^2).

Since force is measured in units of mass times acceleration and stress is measured in units of force per unit area, force and stress do not have the same dimensions.

(c) Angular velocity and frequency:

• Angular velocity is measured in radians per second (rad/s), which represents the rate of change of angular displacement.
• Frequency is measured in Hertz (Hz), which represents the number of cycles or oscillations per second.

Since angular velocity is measured in radians per second and frequency is measured in Hertz, angular velocity and frequency do not have the same dimensions.

(d) Energy and strain:

• Energy is measured in Joules (J), which is a unit of work or the ability to do work.
• Strain, as mentioned before, is a dimensionless quantity.

Since energy is measured in units of work and strain is dimensionless, energy and strain do not have the same dimensions.

In conclusion, none of the given pairs have the same dimensions.