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1.Units, Dimensions and Measurement
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The quantities which have the same dimensions as those of solid angle are:
Astress and angle
Bstrain and arc
Cangular speed and stress
Dstrain and angle
(NEET-2024)
Solution
Solid angle $d \Omega=\frac{d A}{r^2}$ has dimensions $\left[\mathrm{M}^0\left\llcorner^0 \mathrm{~T}^0\right]\right.$
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 $\left[\mathrm{M}^0 \mathrm{~L}^0 \mathrm{~T}^0\right]$
$\theta=\frac{l}{r}$
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 $\left[\mathrm{M}^0 \mathrm{~L}^0 \mathrm{~T}^0\right]$
$\theta=\frac{l}{r}$
Standard 11
Physics
