Question

what are dimensions of work​

Answer 1

The dimensional formula for work is ML²T ¯².

Special Points:-

• Work is a scalar quantity
• The S.I unit is joule.

Answer 2

The dimensions of work are $M^{1} L^{2} T^{-2}$.

Work has only a magnitude but no direction. The formula for work is written as a dot product of force and displacement. Therefore, work is a scalar quantity.

Work is defined as a scalar because it depends on the net distance involved, regardless of the direction. If the object winds up where it started, no work is performed because the distance is zero. So work is the transfer of energy from one body to another in which direction is not important.

The dimensional formula of Work is given by,

$M^{1} L^{2} T^{-2}$

Where,

L = Length

T = Time

Derivation

Work (W) = Force × Displacement........ (1)

Since, Force = Mass × acceleration = M × [L $T^{-2}$]

∴ The dimensional formula of Force = $M^{1} L^{1} T^{-2}$ . . . . (2)

On substituting equation (2) in equation (1) we get,

Work = Force × Displacement

Or, $W=[M^{1} L^{1} T^{-2} ]$×$[M^{0} L^{1} T^{0} ]=$$[M^{1} L^{2} T^{-2} ]$

Therefore, work is dimensionally represented as $[M^{1} L^{2} T^{-2} ]$.

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