(D) The definition of acceleration $(A)$ in terms of length $(L)$ and time $(T)$ is given by the formula: $A = L T^{-2}$. To find the dimensions of le

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(D) The definition of acceleration $(A)$ in terms of length $(L)$ and time $(T)$ is given by the formula: $A = L T^{-2}$. To find the dimensions of length $(L)$ in terms of the given fundamental quantities,we rearrange the formula: $L = A T^2$. Since $A$ and $T$ are chosen as fundamental quantities in the Martian system,the dimension of length is represented as $A T^2$. Therefore,the correct option is $(d)$.

Class 11 Physics Units, Dimensions and Measurement Dimensions and Dimensional Formula

Medium

The Martians use force $(F)$,acceleration $(A)$,and time $(T)$ as their fundamental physical quantities. The dimensions of length in the Martian system are:

A
$F T^2$
B
$F^{-1} T^2$
C
$F^{-1} A^2 T^{-1}$
D
$A T^2$

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Units, Dimensions and Measurement

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Dimensions and Dimensional Formula

If $E$ and $G$ respectively denote energy and gravitational constant,then $\frac{E}{G}$ has the dimensions of :

MediumNEET 2021

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Which one of the following quantities has dimensions different from the remaining three?

Medium

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Let $[{\varepsilon _0}]$ denote the dimensional formula of the permittivity of vacuum. If $M =$ mass,$L =$ length,$T =$ time and $A =$ electric current,then:

MediumJEE MAIN 2013

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Match Column-$1$ with Column-$2$.
Column-$1$ Column-$2$
$(a)$ Wave vector $(i)$ $M^1L^0T^{-3}$
$(b)$ Linear mass density $(ii)$ $M^1L^{-1}T^{-2}$
$(c)$ Intensity of a wave $(iii)$ $M^0L^{-1}T^0$
$(d)$ Volume elasticity coefficient $(iv)$ $M^1L^{-1}T^0$

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The dimensional formula of angular impulse is:

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Column-$1$	Column-$2$
$(a)$ Wave vector	$(i)$ $M^1L^0T^{-3}$
$(b)$ Linear mass density	$(ii)$ $M^1L^{-1}T^{-2}$
$(c)$ Intensity of a wave	$(iii)$ $M^0L^{-1}T^0$
$(d)$ Volume elasticity coefficient	$(iv)$ $M^1L^{-1}T^0$

The Martians use force $(F)$,acceleration $(A)$,and time $(T)$ as their fundamental physical quantities. The dimensions of length in the Martian system are:

Similar Questions

If $E$ and $G$ respectively denote energy and gravitational constant,then $\frac{E}{G}$ has the dimensions of :

Which one of the following quantities has dimensions different from the remaining three?

Let $[{\varepsilon _0}]$ denote the dimensional formula of the permittivity of vacuum. If $M =$ mass,$L =$ length,$T =$ time and $A =$ electric current,then:

Match Column-$1$ with Column-$2$.Column-$1$Column-$2$$(a)$ Wave vector$(i)$ $M^1L^0T^{-3}$$(b)$ Linear mass density$(ii)$ $M^1L^{-1}T^{-2}$$(c)$ Intensity of a wave$(iii)$ $M^0L^{-1}T^0$$(d)$ Volume elasticity coefficient$(iv)$ $M^1L^{-1}T^0$

The dimensional formula of angular impulse is:

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Match Column-$1$ with Column-$2$.
Column-$1$ Column-$2$
$(a)$ Wave vector $(i)$ $M^1L^0T^{-3}$
$(b)$ Linear mass density $(ii)$ $M^1L^{-1}T^{-2}$
$(c)$ Intensity of a wave $(iii)$ $M^0L^{-1}T^0$
$(d)$ Volume elasticity coefficient $(iv)$ $M^1L^{-1}T^0$