Question

If force $F$, acceleration $A$ and time $T$ are taken as fundamental quantities then the dimensions of energy are :

• A. $A^{2}T$
• B. $F{AT}^2$
• C. $F^{2}T$
• D. ${FA}^{-1}{T}^{-1}$

Answer 1

Answer: (B)

$F{AT}^2$

$Energy=$ $F^{\alpha }{A}^{\beta }{T}^{\gamma }$

$M^1{L}^2{T}^{-2}=\left(ML{T}^{-2}{)}^{\alpha }\right(L{T}^{-2}{)}^{\beta }(T{)}^{\gamma }$

$M^1{L}^2{T}^{-2}=M^{\alpha }{L}^{\alpha +\beta }{T}^{-2\alpha -2\beta +\gamma }$

$\alpha =1$

$\alpha +\beta =2$ $\Rightarrow \beta =1$

$-2\alpha -2\beta +\gamma =-2$

$\Rightarrow \gamma =2$

$\Rightarrow Energy=$ $F^1{A}^1{T}^2$