Physical World Units and Measurements - Result Question 6
6. If $x=a t+b t^{2}$, where $x$ is the distance travelled by the body in kilometers while $t$ is the time in seconds, then the unit of $b$ is
(a) $km / s$
(c) $km / s^{2}$
(b) $kms$
(d) $kms^{2}$
[1989]
Topic 2: Dimensions of Physical Quantities
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Answer:
Correct Answer: 6. (c)
Solution:
- (c) Given, $x=a t+b t^{2}$
where, $\quad x=$ distance in $km$
$t=$ time in sec
By the principle of homogencity, the dimensions of each terms of a dimensional equation on both sides are the same.
So, from equation, $x=a t+b t^{2}$
dimension of left side $=[L]$
dimension of right side should be $=[L]$
According to homogeneity’s law,
$ \begin{aligned} & {[L]=[b][T^{2}]} \\ & {[b]=\frac{[L]}{[T^{+2}]}=\text{ dimension of acceleration }} \end{aligned} $
so unit of $b$ should be $km / sec^{2}$.
