Physical World Units and Measurements - Result Question 6

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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

======= ####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

3e0f7ab6f6a50373c3f2dbda6ca2533482a77bed:content/english/neet-pyq-chapterwise/physics/physical-world-units-and-measurements/physical-world-units-and-measurements—result-question-6.md (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:

  1. (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 $km / sec^{2}$.