Question

The S.I. unit of force is written as newton. Newton is written in fundamental units as $kg$ $m/{s^x}$ then the value of x is :
A. 2
B. 3
C. 1
D. -2

Answer 1

Hint: We can easily find the value of $x$ by just knowing the formula. We know that force is defined as the product of mass and acceleration. In order to solve the problem first we need to find the S.I. units of mass and acceleration and then of force. Then on comparing the unit of force we can easily determine the value of $x$.

Complete step by step solution:
We know that
A force can cause an object with mass to change its velocity i.e. to accelerate. A force has both magnitude and direction, making it a vector quantity
Force is defined as the product of mass and acceleration.
Since the unit of force is a derived unit.
So according to definition of force we have,
$F = m \times a$
Where
$m$ = mass of the particle
$a$ = acceleration of the particle
S.I. unit of force is newton = $N$
S.I. unit of mass is kilogram = $kg$
For S.I. unit of acceleration we have
$acceleration = \dfrac{{velocity}}{{time}}$
Since the S.I. unit of velocity is m/s
Therefore S.I. unit of acceleration = $\dfrac{{m/s}}{s} \Rightarrow m/{s^2}$
On putting all the S.I. units in formula of force we have
 S.I. unit of force = $kg \times m/{s^2}$
Newton, $N = kgm/{s^2}$
According to question, $N = kgm/{s^x}$
On comparing we get,
$x = 2$
Hence the value of $x$ is 2

$\therefore$ One newton is the force needed to accelerate one kilogram of mass at the rate of one meter per second squared in the direction of the applied force. Hence the correct option is (A).

Note:
The newton is the International System of Units derived unit of force. It is named after Isaac Newton in recognition of his work on classical mechanics, specifically Newton's second law of motion. There are various types of systems for measuring such as M.K.S, C.G.S. many more including the S.I. system. S.I. system is the most important type of system for measuring.