Question

The SI unit of force is newton. (State whether true or false.)
(A) true
(B) false

Answer 1

Hint: This problem is a textbook example of dimensional analysis. In dimensional analysis we can deduce the value from the dimensional formula of the individual elements by finding the degree of dependence of one physical quantity on the other. The principle of consistency of two expressions can be used to find the equation relating these two quantities. It has some limitations too.

Complete answer:
Force can be defined as the product of mass and acceleration.
Therefore the dimension formula for force can be given as,
[Force]\[=\] [mass] $\times $[acceleration]
[Force] \[=\] [M][MLT$^{-2}$]\[=\][M$^{2}$L T$^{-2}$]
[M$^{2}$L T$^{-2}$] is represented as one newton.
Therefore one newton is the force required to move a body of mass 1 kg with an acceleration of 1 m/s$^{2}$. Newton is represented as N.So, the given statement is true.

Hence, option (A) is the correct answer.

Note:We should know the standard SI unit of some of the known quantities to solve such types of problems. The SI unit of force is Newton. The SI unit of force is Newton while the CGS unit of force is dyne. The relation between 1 Newton and 1 dyne is given as $1N={{10}^{5}}dyne$. Though this method is widely used, there are few drawbacks for this method. Dimensionless quantities cannot be determined by this method. Constant proportionality cannot be determined by this method. It does not apply to trigonometric, logarithmic and exponential functions physical quantities which are dependent upon more than three physical quantities, this method will be difficult.