Question

Force $F=\frac{x}{\rho }+y,$ where $\rho $ is density then dimensional of $x$ and $y$ respectively are :

• A. $\left[M^{2} LT^{- 2}\right],\left[M^{0} L \_{}^{1} T^{0}\right]$
• B. $\left[M^{1} L^{1} T^{- 2}\right],\left[M^{2} L^{2} T^{- 2}\right]$
• C. $\left[M^{2} L^{- 2} T^{- 2}\right],\left[M^{1} L^{1} T^{- 2}\right]$
• D. $\left[M^{1} L^{2} T^{- 2}\right],\left[M^{1} L^{1} T^{- 2}\right]$

Answer 1

Answer: (C)

From the principle of Homogeneity,
$\left[F\right]=\left[\frac{x}{\rho }\right]=\left[y\right]=MLT^{- 2}\left[x\right]=\left[F\right]\left[\rho \right]=\left(M L T^{- 2}\right)\left(M L^{- 3}\right)=M^{2}L^{- 2}T^{- 2}$