Question

On dividing dimension of gravitational constant by the dimension of surface tension we get

• A. $M$
• B. $M{L}^2$
• C. $M^{-2}{L}^3$
• D. None of he above

Answer 1

Answer: (C)

$M^{-2}{L}^3$

By Newton's law of gravitation, $F=\frac{G{m}_1{m}_2}{r^2}$ or $G=\frac{F{r}^2}{m_1{m}_2}$

So, $\left[G\right]=\frac{\left[ML{T}^{-2}\right]\left[L^2\right]}{\left[M\right]\left[M\right]}=\left[M^{-1}{L}^3{T}^{-2}\right]$

Surface tension $=$ force/length or $S=F/l$

So, $\left[S\right]=\frac{\left[ML{T}^{-2}\right]}{\left[L\right]}=\left[M{T}^{-2}\right]$

Thus, $\frac{\left[G\right]}{\left[S\right]}=\frac{\left[M^{-1}{L}^3{T}^{-2}\right]}{\left[M{T}^{-2}\right]}=\left[M^{-2}{L}^3\right]$