Force on a particle in one-dimensional motion is given by F=A v+B t+(C x/A t+D), where F is force, v is speed, t is time, x is position and A, B, C and D are constants. Dimensions of C are [Mp Lq Tr]. Find (p-q-r).

Question

Force on a particle in one-dimensional motion is given by F=A v+B t+(C x/A t+D), where F is force, v is speed, t is time, x is position and A, B, C and D are constants. Dimensions of C are [Mp Lq Tr]. Find (p-q-r). (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

textdim(A)= textdim((F/v)) ; textdim(C)= textdim[(F(A t+D)/x)] ⇒ textdim(C)= textdim[(F/x)((F t/v))]= textdim((F2 t/x v)) = textdim((F2/v2))=[M2 T-2]

Q. Force on a particle in one-dimensional motion is given by $F = A v + Bt + \frac{C x}{A t + D}$ , where $F$ is force, $v$ is speed, $t$ is time, $x$ is position and $A, B, C$ and $D$ are constants. Dimensions of $C$ are $[M^{p} L^{q} T^{r}]$ . Find $(p - q - r)$ .

$dim (A) = dim (\frac{F}{v}); dim (C) = dim [\frac{F ( A t + D )}{x}]$
$\Rightarrow dim (C) = dim [\frac{F}{x} (\frac{Ft}{v})] = dim (\frac{F ^{2} t}{xv})$
$= dim (\frac{F ^{2}}{v ^{2}}) = [M^{2} T^{- 2}]$

Q. Force on a particle in one-dimensional motion is given by F=Av+Bt+At+DCx​, where F is force, v is speed, t is time, x is position and A,B,C and D are constants. Dimensions of C are [MpLqTr]. Find (p−q−r).

dim(A)=dim(vF​);dim(C)=dim[xF(At+D)​] ⇒dim(C)=dim[xF​(vFt​)]=dim(xvF2t​) =dim(v2F2​)=[M2T−2]

Q. Force on a particle in one-dimensional motion is given by $F = A v + Bt + \frac{C x}{A t + D}$ , where $F$ is force, $v$ is speed, $t$ is time, $x$ is position and $A, B, C$ and $D$ are constants. Dimensions of $C$ are $[M^{p} L^{q} T^{r}]$ . Find $(p - q - r)$ .

$dim (A) = dim (\frac{F}{v}); dim (C) = dim [\frac{F ( A t + D )}{x}]$
$\Rightarrow dim (C) = dim [\frac{F}{x} (\frac{Ft}{v})] = dim (\frac{F ^{2} t}{xv})$
$= dim (\frac{F ^{2}}{v ^{2}}) = [M^{2} T^{- 2}]$