Question

Drive the dimension of
1. Surface tension
2. Coefficient of viscosity
3. Pressure
4. Universal gravitational force
5. Young modulus.

Answer 1

1. Surface tension: since

$$\gamma=\frac{1}{2}\frac{F}{L},$$

$$[\gamma]=\frac{M^1L^1T^{-2}}{L^1}=M^1T^{-2}.$$

2. Coefficient of viscosity:

$$F=\mu A\frac{v}{y}, \space\space \implies\space\space \mu=\frac{yF}{vA},,$$

$$[\mu]=\frac{L^1\cdot M^1L^1T^{-2}}{L^1T^{-1}\cdot L^2}=M^1L^{-1}T^{-1}.$$

3. Pressure:

$$p=F/A,$$

$$[p]=\frac{M^1L^1T^{-2}}{L^2}=M^1L^{-1}T^{-2}.$$

4. Universal gravitational force:

$$F=G\frac{M_1}{R^2}M_2=aM_2,$$

$$[F]=M^1L^1T^-2.$$

5. Young modulus:

$$E=\sigma/\epsilon,$$

$$[E]=\frac{M^1L^{-1}T^{-2}}{1}=M^1L^{-1}T^{-2}.$$