SAQ : Establish the relation between (a) joule and erg and (b) kg-m and joule

Question

Establish the relation between (a) joule and erg and (b) kg-m and joule.

Answer

(a) Relation between joule (J) and erg (erg):

1 Joule = 1 N-m = 1 (10⁵ dyne) × (10² cm)

1 Joule = 1 (10⁵ × 10²) dyne-cm

1 Joule = 10⁷ ergs

Therefore, 1 Joule is equal to 10⁷ ergs.

(b) Relation between kilogram-meter (kg-m) and joule (J):

Work = Force × Distance

Force = Mass × Acceleration

Therefore,

Work = Mass × Acceleration × Distance

For the kg-m unit of work, the mass is 1 kilogram, the acceleration is 9.81 m/s^2, and the distance is 1 meter. Therefore, the work done is equal to 9.81 joules.

1 kg-m = 9.81 J