Velocity v (in cm/sec ) of a particle is given in terms of time t (in sec) by relation v = at + frac

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1.Units, Dimensions and Measurement

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The velocity $v$ (in $cm/\sec $) of a particle is given in terms of time $t$ (in sec) by the relation $v = at + \frac{b}{{t + c}}$ ; the dimensions of $a,\,b$ and $c$ are

A

$a = {L^2},\,b = T,\,c = L{T^2}$

B

$a = L{T^2},\,b = LT,\,c = L$

C

$a = L{T^{ - 2}},b = L,\,c = T$

D

$a = L,\,b = LT,\,c = {T^2}$

(AIPMT-2006)

Solution

(c) From the principle of dimensional homogenity $[v] = [at] \Rightarrow [a] = [L{T^{ – 2}}]$.

Similarly $[b] = [L]{\rm{ and}}\;[c] = [T]$

Standard 11

Physics

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