If 1gm cms⁻¹ = x Ns, then number x is equivalent to

The correct option is 1 x 10⁻⁵.

To find the value of the conversion factor $x$, we need to convert the unit of impulse/momentum from the CGS system to the SI system.

First, let us define the relation of the Newton second ($\text{N s}$) in base SI units:

$\text{1 N}=\text{1 kg m s}{-2}^{}$

Therefore, multiplying both sides by seconds ($\text{s}$):

$\text{1 N s}=\text{1 kg m s}{-1}^{}$

Now, let us convert the CGS units (grams and centimeters) to SI units (kilograms and meters):

$\text{1 g}={10}^{-3}\text{kg}$

$\text{1 cm}={10}^{-2}\text{m}$

Substituting these conversion factors into the expression for $\text{1 g cm s}{-1}^{}$:

$\text{1 g cm s}{-1}^{}=\left({10}^{-3}\text{kg}\right)\times \left({10}^{-2}\text{m}\right)\times \text{s}{-1}^{}$

$\text{1 g cm s}{-1}^{}={10}^{-5}\text{kg m s}{-1}^{}$

Since $\text{1 kg m s}{-1}^{}=\text{1 N s}$, we have:

$\text{1 g cm s}{-1}^{}={10}^{-5}\text{N s}$

Comparing this to $\text{1 g cm s}{-1}^{}=x\text{N s}$, we get:

$x=1\times {10}^{-5}$