The dimensional formula for work is [M^1 L^2 T^-2].
The dimensional formula for work is:
Practice Questions
Q1
The dimensional formula for work is:
[M^1 L^2 T^-2]
[M^1 L^1 T^-1]
[M^0 L^2 T^-1]
[M^1 L^0 T^0]
Questions & Step-by-Step Solutions
The dimensional formula for work is:
Step 1: Understand that work is defined as force applied over a distance.
Step 2: Recall that force is calculated using the formula: Force = Mass × Acceleration.
Step 3: The dimensional formula for mass (M) is [M^1].
Step 4: The dimensional formula for acceleration is: Acceleration = Change in velocity / Time. Velocity has the formula: Velocity = Distance / Time.
Step 5: Therefore, the dimensional formula for acceleration is [L^1 T^-2] (since distance is [L^1] and time is [T^1]).
Step 6: Now, substitute the dimensional formula for force: Force = Mass × Acceleration = [M^1] × [L^1 T^-2] = [M^1 L^1 T^-2].
Step 7: Since work is force multiplied by distance, we need to multiply the dimensional formula for force by the dimensional formula for distance, which is [L^1].
Step 8: Therefore, the dimensional formula for work is: [M^1 L^1 T^-2] × [L^1] = [M^1 L^2 T^-2].
Dimensional Analysis – Understanding how physical quantities can be expressed in terms of basic dimensions such as mass (M), length (L), and time (T).
Work in Physics – Work is defined as the product of force and displacement, and its dimensional formula is derived from the dimensions of these quantities.
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