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Find the dimensional formula of the foll...

Find the dimensional formula of the following question :
(a) Surface tension T
(b) Universal constant of gravitation , G
(c ) Impulse ,J
(d) Torque `tau`
The equation involving these equations are :
` T = Fil F = (Gm_(1)m_(2))/(r^(2)), J = F xx t` and `tau = F xx 1 `

Text Solution

Verified by Experts

(a) `T = (F)/(l)`
rArr ` [T] = ([F])/([l]) = ([MLT^(-2)])/([L]) = [MT^(-2)]`
(b)` F= (Gm_(1)m_(2))/(r^(2)) rArr G = (Fr^(2))/(m_(1) m_(2))`
or ` [G] = ([F][r]^(2))/([m]^(2)) = ([MLT^(-2)][L^(2)])/([M^(2)])`
`=[M^(-1)L^(3)T^(-2)]`
(c)` J = F xx t`
`:. [J] = [F][t]`
` = [MLT^(-2)][T]`
`= [MLT^(-1)] `
(d)` tau = F xx l `
`:. [tau] = [F][l]`
`= [ML^(2)T^(2)][L]`
`=[ML^(2)T^(-2)]`
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