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Dimensional Analysis

In the equati...

Question

In the equation of motion, $x = a t + {b t}^{2}$ the units of a and b are respectively (where $x$ is in metres and $t$ is in seconds)

m / s^{2}, m / s

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m / s, m / s^{2}

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m / s, m / s

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m^{2} / s, m / s

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Solution

The correct option is B $m / s, m / s^{2}$
The given equation is $x = a t + b t^{2}$
Units of $x$ , $a t$ and $b t^{2}$ must be equal i.e. $[x] = [a] [t] = [b] [t^{2}]$
$∴$ $[a] = \frac{[x]}{[t]} = \frac{m}{s}$
Also, $[b] = \frac{[x]}{[t^{2}]} = \frac{m}{s^{2}}$

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In the equation of motion, x=at+bt2 the units of a and b are respectively (where x is in metres and t is in seconds)

The correct option is B m/s,m/s2The given equation is x=at+bt2Units of x, at and bt2 must be equal i.e. [x]=[a][t]=[b][t2]∴ [a]=[x][t]=msAlso, [b]=[x][t2]=ms2

In the equation of motion, $x = a t + {b t}^{2}$ the units of a and b are respectively (where $x$ is in metres and $t$ is in seconds)

The correct option is B $m / s, m / s^{2}$
The given equation is $x = a t + b t^{2}$
Units of $x$ , $a t$ and $b t^{2}$ must be equal i.e. $[x] = [a] [t] = [b] [t^{2}]$
$∴$ $[a] = \frac{[x]}{[t]} = \frac{m}{s}$
Also, $[b] = \frac{[x]}{[t^{2}]} = \frac{m}{s^{2}}$