NEET-XII-Physics
14: Some Mechanical Properties of Matter
- #14The dimension ML-1T-2 can correspond to
(a) moment of a force
(b) surface tension
(c) modulus of elasticity
(d) coefficient of viscositydigAnsr: cAns : (c)
​Dimension of modulus of elasticity: `` \frac{{\displaystyle \raisebox{1ex}{$F$}\!\left/ \!\raisebox{-1ex}{$A$}\right.}}{{\displaystyle \raisebox{1ex}{$∆l$}\!\left/ \!\raisebox{-1ex}{$l$}\right.}}=\frac{\left[ML{T}^{-2}\right]}{{L}^{2}}=\left[M{L}^{-1}{T}^{-2}\right]``
Dimension of moment of force: ​`` FL=\left[ML{T}^{-2}\right]\left[L\right]=\left[M{L}^{2}{T}^{-2}\right]``
Dimension of surface tension: ​`` \frac{F}{{\displaystyle L}}=\frac{\left[ML{T}^{-2}\right]}{L}=\left[M{T}^{-2}\right]``
Dimension of coefficient of viscosity: ​`` \frac{FL}{{\displaystyle Av}}=\frac{\left[ML{T}^{-2}\right]\left[L\right]}{\left[{L}^{2}\right]\left[L{T}^{-1}\right]}=\left[M{L}^{-1}{T}^{-1}\right]``
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