Taking force,

Question:

Taking force, length and time to be fundamental quantities find the dimensions of

(a)Density,

(b)Pressure,

(c) momentum and

(d)energy

Solution:

(a) Density $=\frac{\text { mass }}{\text { volume }}=\frac{\frac{\text { force }}{\text { accelearation }}}{\text { volume }}=\left[\mathrm{F} / \mathrm{LT}^{-2}\right]\left[\mathrm{L}^{3}\right]=\left[\mathrm{FL}-4 \mathrm{~T}^{-2}\right]$

(b) Pressure $=$ force/area $=[F] \backslash\left[L^{2}\right]=\left[\mathrm{FL}^{-2}\right]$

(c) Momentum $=\frac{\text { force }}{\text { acceleration }} \times$ velocity $=[\mathrm{F}] /\left[\mathrm{LT}^{-2}\right] \times\left[\mathrm{LT}^{-1}\right]=[\mathrm{FT}]$

(d) Energy $==\overline{\text { acceleration }} \times(\text { velocity })^{2}=[\mathrm{F}] /[\mathrm{LT}-2] \times\left[\mathrm{L}^{2} \mathrm{~T}^{-2}\right]=[\mathrm{FL}]$

Leave a comment

None
Free Study Material