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**Hint:**Here we have to find out the unit of force for the given data. First we have to convert the given data into the required terms. Also, we have to use the formula for finding the unit of force. On doing some simplification we get the required answer.

**Formula used:**

$Force = \dfrac{{length \times mass}}{{tim{e^2}}}$

**Complete step by step answer:**

It is given in the question that the value of the length is $10cm$ which we have to convert to metre

Also, we know that $100cm = 1m$,

Now we convert it into, $10cm = \dfrac{{10}}{{100}} = 0.1m$,

The value of mass is $10gm$which we have to convert to kilogram and we know that $1000g = 1kg$,

So we can change it as, $10g = \dfrac{{10}}{{1000}}$

Take the denominator term $1000 = {10^3}$ we can write it as, $10g = \dfrac{{10}}{{{{10}^3}}}$

$ \Rightarrow 10 \times 10_{}^{ - 3}$

Let us subtract the power terms we get

$ \Rightarrow 10_{}^{ - 2}kg$

The value of time is $0.1s$

Therefore applying the value of $Force = \dfrac{{length \times mass}}{{time_{}^2}}$ and putting the values of length mass and time we get-

Force$ = \dfrac{{0.1 \times 10_{}^{ - 2}}}{{(0.1)_{}^2}}$

Here we can split it as and we get

$ \Rightarrow \dfrac{{10_{}^{ - 3}}}{{10_{}^{ - 2}}}$

Cancelling the same terms and we get the remaining terms,

$ \Rightarrow 10_{}^{ - 1}$

Now the above value we get we can write it as,

$ \Rightarrow \dfrac{1}{{10}}$

Let us divide the terms we get,

$ \Rightarrow 0.1N$

Thus the required unit of force will be equal to $0.1N$.

**Hence, the correct option is $\left( {{A}} \right)$.**

**Note:**It is a simple question where by applying the formula we can solve it. But the main issue arises with calculation because many of us make mistakes in this type of calculation as there is application of inverse also.

Force makes a body to move from rest.

It also helps to increase the speed of a moving body.

It helps to change the direction of a moving body.

It can bring a moving body to rest.

It is a vector quantity.

The basic formula which is used for finding out force is mass x acceleration.

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