Question

what is the dimensions formula for work done , explain step by step​

Answer 1

Solution:

As we know that

Work = FS

Where

F : force

S : distance

Substituting the SI units of Force & distance

→ Work = kgm/s² × m

→ Work = kgm²/s² or Nm or J

Here , N is Newton it is SI unit of Force

Now , writing dimensional formula

Here ,

• kg → M¹
• m² → L²
• 1/s² = s-² → T-²

Now , writing the dimensional formula

Dimensional formula = M¹L²T-²

★ Knowledge enhancer:

SI units

• Force → N or kgm/s²
• Work → J or kgm²/s²
• Energy → J or kgm²/s²
• Time → s
• Mass → kg
• Distance → m
• Momentum → kgm/s
• Temperature → Kelvin

Note: All dimensional formulas are represented by mass , distance & time

Answer 2

Answer:

$\red{ \tt \: ANSWER}$

M1 L-2 T-2

Where,

M = Mass

L = Length

T = Time

$\green{ \bf\: derivation}$

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].

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Therefore, work is dimensionally represented as [M1 L2 T-2].SI unit

joule (J)

Other units

Foot-pound, Erg

In SI base units

1 kg⋅m2⋅s−2

Derivations from

other quantities

W = F ⋅ s

W = τ θ

Dimension

M L2 T−2