Question

In a given system of units, 1 unit of mass= 2kg, 1 unit of length = 5m and 1 unit of time = 5 sec. then in this system, 1N represented:
(A). $\dfrac{5}{2}$ units of force
(B). $\dfrac{2}{5}$ units of force
(C). 2 units of force
(D). $\dfrac{1}{2}$ units of force

Answer 1

Hint: International unit of force is newton. Force is defined as a product of mass and acceleration. Convert kilogram into 1 unit of mass, meter into 1 unit of length and second into 1 unit of time.

Complete step by step solution:
Dimension of force is given by $[M][L][{{T}^{-2}}]$
1 N is represented as $\text{kg m}/{\text{{s}}^{2}}$.
Therefore,
1 N =$[M][L][{{T}^{-2}}]$
$1N=\dfrac{(1kg)(1m)}{(1{{s}^{2}})}$ -------(1)
Values of 1 unit of mass = 2kg, 1 unit of length = 5m and 1 unit of time = 5sec can be written as,
1 unit of mass = 2kg
1 unit of mass = $2\times 1kg$
So 1kg = $\dfrac{1}{2} \text{unit of mass}$
1 unit of length = 5m
1 unit of length = $5\times 1m$
So, $1m=\dfrac{1}{5} \text{unit of length}$
1 unit of time = 5sec
I unit of time = $5\times 1\sec$
$1\sec =\dfrac{1}{5} \text{unit of time}$
Now put values of 1 unit of mass = 2kg, 1 unit of length = 5m and 1 unit of time = 5sec in equation (1)i.e. in above formula,
1 N = $\dfrac{(\dfrac{1}{2} \text{unit of mass})(\dfrac{1}{5} \text{unit of mass})}{(\dfrac{1}{5} \text{unit of mass})}$
1 N$=\dfrac{5}{2} \text{unit of mass}$
So one newton of force is $\dfrac{5}{2}$ unit of force.
So, the answer is $\dfrac{5}{2}$ unit of force

Note: SI unit of force is newton. It is represented by N. one newton is also represented as a kilogram meter per second square. Force is a vector quantity which has both magnitude and direction. Force is dependent on mass and acceleration.