The dimensional formula of Stress is
[ M1 L-1 T-2 ]
where [M], [L], and [T] are the fundamental quantities: Mass, Length, and Time.
Now let’s see how we can drive this formula.
How to calculate the dimensional formula of stress?
In physics, we can define stress as the force acting upon a small bounded area. So mathematically,
Stress = Force / Area
We know that formula of Force is mass * acceleration. Now let’s substitute this value in the above equation,
Stress = (mass * acceleration) / Area
Also, we can further derive acceleration.
- acceleration = speed / time
- speed = displacement / time
- acceleration = displacement / time2
After substituting the value of acceleration, our formula becomes
Stress = (mass * displacement / time2 ) / Area
Similarly, we know that Area is equal to length * breadth, so our formula becomes
Stress = (mass * displacement / time2 ) / (length * breadth) = (mass * displacement) (length * breadth * time2) = mass * displacement * length-1 * breadth-1 * time-2 = mass * displacement * length-1 * breadth-1 * time-2
Dimensionally, we use
- [M] to represent mass
- [L] for displacement, length, and breadth
- and [T] for time.
Now our formula becomes,
Stress = [M1] * [L1] * [L-1] * [L-1] * [T-2] = [M1] * [L-1] * [T-2]
Hence, the dimensional formula of Stress is [ M1 L-1 T-2 ].
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