Question

One Newton is the force that produces an acceleration of
A. \[1\] \[m{s^{ - 2}}\]on a mass of \[1\]g
B. \[1\] \[c{m^{ - 2}}\] on a mass of \[1\] Kg
C. \[1\] \[c{m^{ - 2}}\]on a mass of \[1\] g
D. \[1\] \[m{s^{ - 2}}\]on a mass of \[1\] Kg

Answer 1

Hint: According to Newton’s second law of motion, Force = mass*acceleration. In the equation both the left hand side and right hand side of the equation should be in the same system of units. In this question since \[1\]Newton is in the SI units both the acceleration and mass should also be mentioned in the SI system.
Formula used:
 Force = mass*acceleration

Complete step by step answer:
The unit of force in SI system is Newton.
Equation of force, Force = mass* acceleration
Rearranging, acceleration= Forcemass
\[1\]N= \[1\]Kg\[m{s^{ - 2}}\]and the SI unit of mass is Kg.
Substituting the SI units in the equations
We get, acceleration = \[\dfrac{{1kgm{s^{ - 2}}}}{{1kg}}\] = \[1\] \[m{s^{ - 2}}\],
In this option acceleration (\[m{s^{ - 2}}\]) is in the SI unit but mass is mentioned in g which is in the CGS system. Both acceleration and mass should be in the same unit of system.
In this option acceleration (\[c{m^{ - 2}}\]) is written in the CGS format and the mass, Kg is in the SI unit. In this option too acceleration and mass are written in different units of systems.
The units of both acceleration and mass are in the CGS system. However, \[1\] Newton is in the SI unit format. Both the left and right hand side of an equation should be in the same system
Both the units are in the SI system. Hence this is the correct option.\[\]

So the correct option is (D)

Note: In the general form, from Newton’s second law $F = \dfrac{{dP}}{{dt}}$, that is the rate of change of momentum of a particle is given by the force acting on it. Substituting momentum=mass*acceleration (\[P = mv\]). We get \[F = ma\] . If $F = \dfrac{{dP}}{{dt}} = 0$, then there is no force acting on the body. Therefore momentum must be constant or conserved.