(A) Let the dimension of mass be $m = k \cdot t^a \cdot u^b \cdot I^c$,where $k$ is a dimensionless constant.Substituting the dimensions of each quant

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(A) Let the dimension of mass be $m = k \cdot t^a \cdot u^b \cdot I^c$,where $k$ is a dimensionless constant.Substituting the dimensions of each quantity:$[M^1 L^0 T^0] = [T]^a [L T^{-1}]^b [M L^2 T^{-1}]^c$$[M^1 L^0 T^0] = [M^c] [L^{b+2c}] [T^{a-b-c}]$Comparing the powers of $M$,$L$,and $T$ on both sides:For $M$: $c = 1$For $L$: $b + 2c = 0 \implies b + 2(1) = 0 \implies b = -2$For $T$: $a - b - c = 0 \implies a - (-2) - 1 = 0 \implies a + 1 = 0 \implies a = -1$Therefore,the dimension of mass is $[t^{-1} u^{-2} I^1]$.

Class 11 Physics Units, Dimensions and Measurement Dimensional Analysis, Uses and Limitations

Medium

If time $(t)$,velocity $(u)$,and angular momentum $(I)$ are taken as the fundamental units,then the dimension of mass $(m)$ in terms of $(t)$,$(u)$,and $(I)$ is:

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$[t^{-1} u^{-2} I^{1}]$
B
$[t^{1} u^{2} I^{-1}]$
C
$[t^{-2} u^{-1} I^{1}]$
D
$[t^{-1} u^{1} I^{-2}]$

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Dimensional Analysis, Uses and Limitations

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If time $(t)$,velocity $(u)$,and angular momentum $(I)$ are taken as the fundamental units,then the dimension of mass $(m)$ in terms of $(t)$,$(u)$,and $(I)$ is:

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If $E$ and $E_0$ represent the energies, and $t$ and $t_0$ represent the times, which of the following relations is dimensionally correct?

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