Force $(F)$ and density $(d)$ are related as $F\, = \,\frac{\alpha }{{\beta \, + \,\sqrt d }}$ then dimension of $\alpha $ and $\beta$ are
- A$M^{3/2} L^{-1/2} T^{-2}, M^{1/2} L^{-3/2} T^0$
- B$M^{1/2 }L^{-3/2} T^{-2}, M^{-3/2} L^{-3/2} T^0$
- C$M^{3} L^{-1} T^{-2/3}, M^{2} L^{-3} T^{2}$
- D$M^{2} L^{-1/2} T^{-2}, M^{3/2} L^{-1/2} T^0$
Similar Questions
If momentum $(P),$ area $(A)$ and time $(T)$ are taken to be the fundamental quantities then the dimensional formula for energy is :
- [JEE MAIN 2020]
The velocity of water waves $v$ may depend upon their wavelength $\lambda $, the density of water $\rho $ and the acceleration due to gravity $g$. The method of dimensions gives the relation between these quantities as
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Given that $\int {{e^{ax}}\left. {dx} \right|} = {a^m}{e^{ax}} + C$, then which statement is incorrect (Dimension of $x = L^1$) ?
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Consider following statements
$(A)$ Any physical quantity have more than one unit
$(B)$ Any physical quantity have only one dimensional formula
$(C)$ More than one physical quantities may have same dimension
$(D)$ We can add and subtract only those expression having same dimension
Number of correct statement is
Consider following statements
$(A)$ Any physical quantity have more than one unit
$(B)$ Any physical quantity have only one dimensional formula
$(C)$ More than one physical quantities may have same dimension
$(D)$ We can add and subtract only those expression having same dimension
Number of correct statement is
In a system of units if force $(F)$, acceleration $(A) $ and time $(T)$ are taken as fundamental units then the dimensional formula of energy is
In a system of units if force $(F)$, acceleration $(A) $ and time $(T)$ are taken as fundamental units then the dimensional formula of energy is