If force ({F}), length ({L}) and time ({T}) a | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

$	ext { Density }=\left[{F}^{{a}} {L}^{{b}} {T}^{{c}}ight]$

${\left[{ML}^{-3}ight]=\left[{M}^{{a}} {L}^{{a}} {T}^{-2 {a}} {L}^{{b}} {T}^{{c}}\

Vedclass · Accepted Answer

$\left[{FL}^{-4} {T}^{2}\right]$

Vedclass · Answer

$	ext { Density }=\left[{F}^{{a}} {L}^{{b}} {T}^{{c}}ight]$

${\left[{ML}^{-3}ight]=\left[{M}^{{a}} {L}^{{a}} {T}^{-2 {a}} {L}^{{b}} {T}^{{c}}ight]}$

${\left[{M}^{1} {L}^{-3}ight]=\left[{M}^{{a}} {L}^{{a}+{b}} {T}^{-2 {a}+c}ight]}$

${a}=1 ; \quad {a}+{b}=-3 \quad ; \quad-2 {a}+{c}=0$

$\quad 1+{b}=-3 \quad {c}=2 {a}$

${b}=-4 \quad {c}=2$

So, density $=\left[{F}^{1} {L}^{-4} {T}^{2}ight]$

If force $({F})$, length $({L})$ and time $({T})$ are taken as the fundamental quantities. Then what will be the dimension of density

Similar Questions

The period of a body under SHM i.e. presented by $T = {P^a}{D^b}{S^c}$; where $P$ is pressure, $D$ is density and $S$ is surface tension. The value of $a,\,b$ and $c$ are

A force defined by $F=\alpha t^2+\beta t$ acts on a particle at a given time $t$. The factor which is dimensionless, if $\alpha$ and $\beta$ are constants, is:

If force $[F],$ acceleration $[A]$ and time $[T]$ are chosen as the fundamental physical quantities. Find the dimensions of energy.

Using dimensional analysis, the resistivity in terms of fundamental constants $h, m_{e}, c, e, \varepsilon_{0}$ can be expressed as