Physics MCQs for NEET — Practice Questions with Answers

Quantities having different dimensions can only be divided or multiplied but they cannot be added or subtracted.

Angle of banking : $\tan \theta =\frac{v^2}{rg}$. i.e. $\frac{v^2}{rg}$ is dimensionless.

Solar constant is energy received per unit area per unit time i.e. $\frac{\left[M{L}^2{T}^{-2}\right]}{\left[L^2\right]\left[T\right]}=\left[M^1{T}^{-3}\right]$ 

From the principle of dimensional homogenity $\left[a\right]=\left[\frac{F}{t}\right]=\left[ML{T}^{-3}\right]$ and $\left[b\right]=\left[\frac{F}{t^2}\right]=\left[ML{T}^{-4}\right]$

$K=Y\times r_0$ = $\left[M{L}^{-1}{T}^{-2}\right]\times \left[L\right]$ = $\left[M{T}^{-2}\right]$

Y = Young's modulus and $r_0$ = Interatomic distance

Let $\left[G\right]\propto c^x{g}^y{p}^z$

by substituting the following dimensions :

$\left[G\right]=\left[M^{-1}{L}^3{T}^{-2}\right],\left[c\right]=\left[L{T}^{-1}\right],\left[g\right]=\left[L{T}^{-2}\right]$

$\left[p\right]=\left[M{L}^{-1}{T}^{-2}\right]$

and by comparing the powers of both sides

we can get $x=0,y=2,z=-1$

$\therefore \left[G\right]\propto c^0{g}^2{p}^{-1}$  

Let $T\propto S^x{r}^y{\rho }^z$

by substituting the dimension of $\left[T\right]=\left[T\right]$

$\left[S\right]=\left[M{T}^{-2}\right],\left[r\right]=\left[L\right],\left[\rho \right]=\left[M{L}^{-3}\right]$

and by comparing the power of both the sides

$x=-1/2,y=3/2,z=1/2$

so $T\propto \sqrt{\rho r^3/S}\Rightarrow T=k\sqrt{\frac{\rho r^3}{S}}$ 

Resistivity $\left[\rho \right]=\frac{\left[R\right].\left[A\right]}{\left[l\right]}\text{where }\left[R\right]=\left[M{L}^2{T}^{-1}{Q}^{-2}\right]$

$\therefore \left[\rho \right]=\left[M{L}^3{T}^{-1}{Q}^{-2}\right]$  

$I=\frac{Q}{t}=\frac{\left[Q\right]}{\left[T\right]}=\left[M^0{L}^0{T}^{-1}Q\right]$ 

Torque = $\left[M{L}^2{T}^{-2}\right]$, Angular momentum = $\left[M{L}^2{T}^{-1}\right]$

So mass and length have the same dimensions.