Dimensional Formula of Spring Constant
In this article, we will find the Dimensional Formula of Spring constant
Dimensional formula for is
$[M^1L^0T^{-2}]$
Where
M -> Mass
L -> Length
T -> Time
We would now derive this dimensional formula.
Derivation for expression of Dimension of Spring Constant
Spring constant is given as per the Hooke’s law as
$F= kx$
Where x -> displacement of the spring
F -> Force applied on the Spring
k-> Spring constant of the spring
So,
$k= \frac {F}{x}$
Now the dimension of displacement= $[L^1]$
Lets derive the dimension of Force
$F= ma$
Now
Where m-> mass
a -> Acceleration
Dimension of Mass = $[M^1]$
Now acceleration
$a = \frac {\Delta v}{t}$
Now dimension of Velocity= $[M^0 L^1T^{-1}]$
dimension of Time = $[M^0 T^1]$
So dimension of Acceleration = $ \frac {[M^0 L^1T^{-1}]}{ [M^0 T^1]}= [M^0 L^1T^{-2}]$
So, Dimension of force is given by
$\text {Dimension of Force} =[M^1] \times [M^0 L^1T^{-2}] = [M^1L^1T^{-2}]$
Now we know both the displacement and Force dimension , we can calculate the spring constant dimension easily as
$\text {dimension of spring constant} = \frac { \text {dimension of force}} { \text {dimension of displacement}}$
$= \frac {[M^1L^1T^{-2}]}{[L^1]} = [M^1L^0T^{-2}]$
Unit of Spring constant is Newton/meter.
Try the free Quiz given below to check your knowledge of Dimension Analysis:-
Quiz on Dimensional Analysis
Related Articles and references
- New Simplified Physics by SL Arora : I highly recommend this book for class 11 Physics students. It is easy to understand with lots of solved problems.
- Dimensional Analysis:- a very good website for physics concepts
- dimension of Density
- Dimension of Force
- Dimensional Formula of Work
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