Q103 / 200 · NEET 2024 · Physics

The quantities which have the same dimensions as those of solid angle are:

  • A
    stress and angle
  • B
    strain and arc
  • C
    angular speed and stress
  • Correct answer
    D
    strain and angle

Solution

Solid angle $d \Omega=\frac{d A}{r^2}$ has dimensions $\left[\mathrm{M}^0 \mathrm{~L}^0 \mathrm{~T}^0\right]$ Strain $=\frac{\Delta l}{l}$ has dimensions $\left[\mathrm{M}^0 \mathrm{~L}^0 \mathrm{~T}^0\right]$ Angle measured in radians is also dimensionless $\left[\mathrm{M}^0 \mathrm{~L}^{\circ} \mathrm{T}^0\right]$ $\theta=\frac{I}{r}$

Hence, the correct answer is option: 'D'.

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