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1.Units, Dimensions and Measurement
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The position of a particle at time $t$ is given by the relation $x(t) = \left( {\frac{{{v_0}}}{\alpha }} \right)\,\,(1 - {e^{ - \alpha t}})$, where ${v_0}$ is a constant and $\alpha > 0$. The dimensions of ${v_0}$ and $\alpha $ are respectively
A
${M^0}{L^1}{T^{ - 1}}$ and ${T^{ - 1}}$
B
${M^0}{L^1}{T^0}$ and ${T^{ - 1}}$
C
${M^0}{L^1}{T^{ - 1}}$ and $L{T^{ - 2}}$
D
${M^0}{L^1}{T^{ - 1}}$ and $T$
Solution
(a) Dimension of $\alpha t$$=$ $[{M^0}{L^0}{T^0}]$ $\therefore [\alpha] = [{T^{ – 1}}]$
Again $\left[ {\frac{{{v_0}}}{\alpha }} \right] = [L]$so $[{v_0}] = [L{T^{ – 1}}]$
Standard 11
Physics
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