Which of the following pair does not have similar dimensions ?

The correct answer is tension and surface tension.

To determine which pair of physical quantities does not have similar (identical) dimensions, we can analyze the dimensional formulas for each option step-by-step:

1. Stress and Pressure:
- Pressure ($P$) is defined as force per unit area:
$P=\frac{F}{A}$
The dimensional formula for force ($F$) is $\left[ML{T}^{-2}\right]$ and for area ($A$) is $\left[L^2\right]$.
Thus, the dimensions of pressure are:
$\left[\mathrm{Pressure}\right]=\frac{\left[ML{T}^{-2}\right]}{\left[L^2\right]}$
- Stress is also defined as restoring force per unit area, so it shares the exact same dimensional formula:
$\left[\mathrm{Stress}\right]=\left[M{L}^{-1}{T}^{-2}\right]$
Therefore, stress and pressure have similar dimensions.

2. Angle and Strain:
- Angle ($\theta$) is measured as arc length divided by radius:
$\theta =\frac{\mathrm{Arc\; length}}{\mathrm{Radius}}$
Since both arc length and radius are lengths, the dimensions are:
$\left[\mathrm{Angle}\right]=\frac{\left[L\right]}{\left[L\right]}$ (dimensionless)
- Strain is defined as the change in dimension divided by the original dimension (e.g., change in length over original length):
$\mathrm{Strain}=\frac{\Delta L}{L}$
This is also a ratio of two identical physical quantities, so it is dimensionless:
$\left[\mathrm{Strain}\right]=\left[M^0{L}^0{T}^0\right]$
Therefore, angle and strain both have similar dimensions (they are both dimensionless).

3. Tension and Surface Tension:
- Tension is a pulling force exerted by a string, cable, or chain. Since it is a force, its dimensional formula is:
$\left[\mathrm{Tension}\right]=\left[ML{T}^{-2}\right]$
- Surface tension ($T$) is defined as force per unit length:
$\mathrm{Surface\; Tension}=\frac{\mathrm{Force}}{\mathrm{Length}}$
Its dimensional formula is:
$\left[\mathrm{Surface\; Tension}\right]=\frac{\left[ML{T}^{-2}\right]}{\left[L\right]}$
Comparing the two, we see that $\left[ML{T}^{-2}\right]\ne \left[M{T}^{-2}\right]$. Thus, tension and surface tension do not have similar dimensions.

4. Planck's constant and Angular momentum:
- Planck's constant ($h$) can be derived from the energy equation $E=h\nu$, where $\nu$ is frequency (dimension of $\left[T^{-1}\right]$) and $E$ is energy (dimension of $\left[M{L}^2{T}^{-2}\right]$):
$\left[h\right]=\frac{\left[E\right]}{\left[\nu \right]}$
- Angular momentum ($L$) is given by the formula $L=r\times p=r\times \left(mv\right)$:
$\left[L\right]=\left[L\right]·\left[M\right]·\left[L{T}^{-1}\right]=\left[M{L}^2{T}^{-1}\right]$
Therefore, Planck's constant and angular momentum share identical dimensions.

Conclusion:
The pair that does not have similar dimensions is tension and surface tension.