Question

If \[1\,gcm{s^{ - 1}} = x\,Ns\] then what is the value of \[x\] ?

Answer 1

Hint: To solve this problem learn the definition of force, learn the definition of one Newton and simple unit conversion to calculate the value. \[1\,N\] is said to be applied when a body is moving with unit acceleration with a mass of one kilogram

Formula used:
\[1N\] of force is said to be applied when a body of mass \[1\,kg\] moves with an acceleration of \[1\,m{s^{ - 2}}\].
So, \[1\,N = 1\,m{s^{ - 2}}.1\,kg\]
\[1\,kg\] is equal to \[1000\,g\]. \[1\,m\] of length is equal to \[100\,cm\].

Complete step by step answer:
We have given here, \[1\,gcm{s^{ - 1}} = x\,Ns\]. Now, we have to find the value of \[x\]. Now, we know that the value of \[1\,N\] is the force applied to a body of mass \[1kg\]moving with an acceleration of \[1\,m{s^{ - 2}}\]. So, we can write, \[1\,N = 1\,m{s^{ - 2}}.1kg\].So, putting the value, we can have,
\[1\,gcm{s^{ - 1}} = x \cdot 1m{s^{ - 2}} \cdot 1\,kgs\]
Now, \[1\,kg\] of mass is equal to \[1000\,g\] and \[1\,m\] of length is equal to \[100\,cm\].So, putting the values and further simplifying we have,
\[1\,gcm{s^{ - 1}} = x \cdot 100 \cdot 1000\,gcm{s^{ - 1}}\]
\[\Rightarrow x{10^5} = 1\]
\[\therefore x = {10^{ - 5}}\]

So, the value of \[x\] is \[{10^{ - 5}}\].

Note: The term \[1\,Ns\] is nothing but the change is in momentum of the body or the impulse of the body. The change in momentum of the body per unit time is called the force contrast to that the change in momentum of the body is called the impulse of force. Momentum is nothing the mass times the velocity of the body. So, \[1\,Ns\] means that the change in momentum of the body is \[1\,kgm{s^{ - 1}}\] or simply if the velocity of a body of mass \[1\,kg\] changes by \[1\,m{s^{ - 1}}\]then the momentum of the body is \[1\,Ns\].