Question

The value of $g$ is $9.8\,m{s^{ - 2}}$. Its value in a new system in which the unit of length in kilometer and that of time in a minute, is:
A) $35.3$ km-minute²
B) $3.53$ km-minute²
C) $353$ km-minute²
D) $0.353$ km-minute²

Answer 1

Hint: To solve the question, you simply need to convert the units of the acceleration due to gravity on both, the numerator and the denominator, from meters to kilometers and from seconds to hours, respectively. Remember that $60$ seconds make a minute and similarly, $60$ minutes make an hour.

Complete step by step answer:
We will try to solve the question exactly as we described in the hint section of the solution to the asked question. We’ll simply try to convert the units correctly on both sides, the numerator and the denominator of the units of the acceleration due to gravity $\left( g \right)$ .
To find the answer, we need to convert meter into kilometer and second into hours. For this, we need the basic correlation between them which are mentioned below:
We already know that:
$1000\,m = 1\,km$
Hence, we can divide both sides by thousand and can find what a meter values in kilometers as:
$\Rightarrow$ $1\,m = {10^{ - 3}}\,km$
Now, we need to convert seconds into minutes.
We already know that a minute is nothing but a collection of sixty seconds, similarly, an hour is nothing but a collection of sixty minutes. Hence, we can write that:
$\Rightarrow$ $60\,s = 1$ minute
Now again, we can divide both sides by sixty to find how we can write one second in terms of minutes as:
$\Rightarrow$ $1\,s = \dfrac{1}{{60}}$ minutes
Now, all we need to do is to substitute the found-out values of meter in kilometers and second in minutes in the value of acceleration due to gravity, $g = 9.8\,m{s^{ - 2}}$
We have been told that:
$\Rightarrow$ $g = 9.8\,m{s^{ - 2}}$
Now, substituting the following terms in the value of $g$ :
$\Rightarrow$ $1\,m = {10^{ - 3}}\,km$
$\Rightarrow$ $1\,s = \dfrac{1}{{60}}$ minutes
$\Rightarrow$ $g = 9.8 \times \dfrac{{{{10}^{ - 3}}}}{{{{\left( {\dfrac{1}{{60}}} \right)}^2}}}$ km-minute²
Upon solving, we get:
$g = 35.3$ km-minute²
Hence, the correct option is the option (A) as the value matches with the value that we just found out upon solving the question.

Note: Such questions mainly need you to manipulate the units and convert them into other units, for this, some major relation that you should know are:
$
  1\,hour = 60\,m\, = 3600\,s \\
  1\,km = 1000\,m = \,{10^5}\,cm \\
  1\,litre = 1000\,ml = 1000\,cc \\
 $