The velocity of a particle depends upon time | vedclass

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(A) According to the principle of homogeneity of dimensions,only physical quantities with the same dimensions can be added or subtracted.Since $v$ is

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$m/s$

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(A) According to the principle of homogeneity of dimensions,only physical quantities with the same dimensions can be added or subtracted.Since $v$ is velocity and $v = a + bt + ct^2$,the dimensions of each term on the right-hand side must be equal to the dimensions of velocity $(v)$.Therefore,the dimension of $a$ must be equal to the dimension of $v$.Since the unit of velocity $v$ is $m/s$,the unit of $a$ must also be $m/s$.

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 velocity of a particle depends upon time as $v = a + bt + ct^2$. If the velocity is in $m/s$,the unit of $a$ will be:

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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 $(iv)$ $M^1L^{-1}T^0$

Define dimensional formula and dimensional equation by using suitable examples.

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