Dimension and Units of Work
Category : JEE Main & Advanced
Dimension : As work = Force ´ displacement
[W]\[=[ML{{T}^{-2}}]\times [L]=[M{{L}^{2}}{{T}^{-2}}]\]
Units : The units of work are of two types
| Absolute units | Gravitational units |
|
Joule [S.I.]: Work done is said to be one Joule, when 1 Newton force displaces the body through 1 metre in its own direction. From, W = F.s 1 Joule = 1 Newton x 1 m |
kg-m [S.I.]: 1 kg-m of work is done when a force of 1kg-wt. displaces the body through 1m in its own direction. From W = F s 1 kg-m = 1 kg-wt x 1 m = 9.81 N x 1 metre = 9.81 Joule |
|
erg [C.G.S.] : Work done is said to be one erg when 1 dyne force displaces the body through 1 cm in its own direction. From W = F s \[1\,erg=1dyne\times 1cm\] Relation between Joule and erg 1 Joule = 1 N x 1 m = \[{{10}^{5}}\] dyne x \[{{10}^{2}}\] cm = \[{{10}^{7}}\] dyne x cm = \[{{10}^{7}}\] erg |
gm-cm [C.G.S.] : 1 gm-cm of work is done when a force of 1gm-wt displaces the body through 1cm in its own direction. From W = F s 1 gm-cm = 1gm-wt x 1cm. = 981 dyne x 1cm = 981 erg |
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