Question 223: Units , Dimensions and Error Analysis

Question

Identify the pair whose dimensions are equal

Accepted Answer

To determine which pairs have equivalent dimensions, we examine the respective dimensional formulas.
For work (W) specified as $ \overrightarrow{F} \cdot \overrightarrow{s} $:
$ W = F s \cos 	heta $
The dimensions are:
$ W = [MLT^{-2}][L] = [ML^2T^{-2}] $
For torque ($\overrightarrow{	au}$) given as $ \overrightarrow{r} 	imes \overrightarrow{F} $:
$ 	au = rF \sin 	heta $
The dimensions are:
$ 	au = [L] [MLT^{-2}] = [ML^2T^{-2}] $
Therefore, the dimensions of torque and work are identical.

Answer

torque and work

Answer

stress and energy

Answer

force and stress

Answer

force and work

Units , Dimensions and Error Analysis

Identify the pair whose dimensions are equal

Choose the correct answer: