Question

In a system of units the units of mass, length and time are 1 quintal, 1Km, and 1h respectively. In this system, 1N force will be equal to
(A) $1$ units
(B) $129.6$ units
(C) $427.6$ units
(D) $60$ units

Answer 1

The above problem can be solved by converting them to the universal dimensional measurements and the formula that was derived from Newton’s second law of motion, which incorporates the mass, the length, and the time is taken by an object in a system.

Formula used:
The formula for finding the value of $1\,N$ is given by the newton’s second law of motion;
$F = ma$
Where, $F$ denotes the force exerted by the object, $m$ denotes the mass of the object, $a$ denotes the acceleration of the object.

Complete step by step answer:
The data given in the problem are;
The mass of the object in a system is $m = 1$ quintal.
Length of the object in a system is, $l = 1\,\,Km$.
Time taken by the object in a system is, $t = 1\,\,h$

By using the newton’s second law of motion;
$F = ma$
By assuming the standard units for all the units used in the above formula;
$\Rightarrow 1\,\,Kg = {10^{ - 2}}$ quintal
$\Rightarrow 1\,\,m = {10^{ - 3}}\,\,Km \\\ \Rightarrow 1\,\,s = {\left( {\dfrac{1}{{3600}}} \right)^2}\,\,hr \\\$
Therefore,
$\Rightarrow 1\,\,N = \dfrac{{Kg\,\,m}}{{{s^2}}}\,\,..........\left( 1 \right)$
Since, $a = \dfrac{m}{{{s^2}}}$
Substitute the appropriate values in the units;
$\Rightarrow 1\,\,N = \dfrac{{{{10}^{ - 2}} \times {{10}^{ - 3}}}}{{{{\left( {\dfrac{1}{{3600}}} \right)}^2}}}$
On equating the above equation, we get;
$\Rightarrow 1\,\,N = 129.6$ units.

$\therefore$ In this system, $1N$ Force will be equal to $129.6$ units. Hence the option (B) is the correct answer.

Note:
Newton’s second law of motion denotes that the acceleration of an object as produced by a total force is directly proportional to the magnitude of the total force, in the same direction as the total force, and inversely proportional to the mass of the object.