Find the dimensions of acceleration & work
Answers
Answer:
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Answer:
Dimensional Formula of Acceleration
The dimensional formula of acceleration is given by,
M0 L1 T-2
Where,
M = Mass
L = Length
T = Time
Derivation
Acceleration (a) = Velocity × Time-1 . . . . . (1)
Since, Velocity (V) = Displacement × Time-1
∴ The dimensional formula of velocity is [M0 L1 T-1] . . . . (2)
On substituting equation (2) in equation (1) we get,
Acceleration = Velocity × Time-1
Or, a = [M0 L1 T-1] × [T] = [M0 L1 T-2]
Therefore, acceleration is dimensionally represented as [M0 L1 T-2].
The dimensional formula of Work is given by,
M1 L-2 T-2
Where,
M = Mass
L = Length
T = Time
Derivation
Work (W) = Force × Displacement . . . . . (1)
Since, Force = Mass × acceleration = M × [L T-2]
∴ The dimensional formula of Force = M1 L1 T-2 . . . . (2)
On substituting equation (2) in equation (1) we get,
Work = Force × Displacement
Or, W = [M1 L1 T-2] × [M0 L1 T0] = [M1 L2 T-2].
Therefore, work is dimensionally represented as [M1 L2 T-2].