Question

If the unit of force is kN, the length is 1 km and for the time it is 100s, then what will be the unit of mass?
(A) 1000 kg
(B) 1 kg
(C) 10000 kg
(D) 100 kg

Answer 1

Hint: We know the standard SI unit of force is newtons (N), for length it is meters (m) and for time it is seconds (s). Now we are given that the unit of force is to be kilo Newton, for length it is 1km and for time it is 100s. we can make use of dimensional analysis to solve this problem.

Complete step by step solution:
We know force is given by the formula, $F=ma$
$$F=[ML{T}^{-2}]$$
$$\begin{gathered} \Rightarrow 1000N={\displaystyle \frac{M\times 1000m}{{(100s)}^2}} \\ \Rightarrow M=10000kg \end{gathered}$$
So, the correct option is (c)

Additional Information: Method of Dimensional analysis is also called Factor Label Method. The method of dimensional analysis is of great use as we can check the correctness of Physical Equation by using it. However, it should be kept in mind that dimensional analysis cannot help us determine any dimensionless constants in the equation. The method when used in chemistry there in place of using designated symbols we use units.

Note: There are few drawbacks for this method, although this method is widely used. This method cannot be used when we are dealing with the dimensionless quantities. 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.