Question

Ramu applied a force of 10N on a body to move it from rest. He wants to express the applied force in terms of the various systems of the unit. Express $10\;N$ force in terms of kgf.
(A) $98\;kgf$
(B) $56\;kgf$
(C) $1.02\;kgf$
(D) $84\;kgf$

Answer 1

In this question, the concept of the conversion factor for the force will be used. As we know that kgf is the force applied on $1\;kg$ mass in earth’s gravity. Based on this concept we can calculate any amount of force in kgf if the force is given in Newton. the value of $g$ is $9.8\;m/{s^2}$.

Complete step by step answer:
In this question, as we know that the force is an external agent which is used for changing the state or shape of a body. The SI unit of force is Newton which is represented as $N$.
The value of acceleration due to gravity on the earth’s surface is $9.8\;m/{s^2}$.
One kilogram force unit is defined as the amount of force applied on a one kilogram mass within the earth’s gravitational field.
Let us assume the mass is to be assumed $1\;kg$.
In mathematical terms we can express this as,
$\Rightarrow 1\;N = \dfrac{{1\;kg}}{{9.8\;m/{s^2}}}$
We will simplify the t above expression to obtain the simplified form as,
$\Rightarrow 1\;N = 0.102\;kgf$
As per the given question, we need to convert $10\;N$ force in kgf.
Now, we will multiply both sides of the above equation by $10$.
$\Rightarrow 1\;N\left( {10} \right) = 0.102\;kgf\left( {10} \right)$
Further simplify the above expression we obtain,
$\therefore 10\;N = 1.02\;kgf$
Hence, the applied force is in terms of kgf of the unit is $1.02\;kgf$

Therefore, the correct option is C.

Note: In this question we should remember the value of acceleration due to gravity and the definition of one-kilogram force is needed to solve this question. If the wrong definition is used in solving this question, then the result will also be wrong.