If dimensions of critical velocity v_c of a liquid flowing through a tube are expressed as $\left[{\mathrm{\eta }}^{\mathrm{x}}{\mathrm{\rho }}^{\mathrm{y}}{\mathrm{r}}^{\mathrm{z}}\right]$, where $\mathrm{\eta }, \mathrm{\rho } \mathrm{and} \mathrm{r}$ are the coefficient of viscosity of the liquid, the density of liquid and radius of the tube respectively, then the values of x, y and z, respectively, will be

1. 1, -1, -1

2. -1, -1, 1

3. -1, -1, -1

4. 1, 1, 1,

If force (F), velocity (v) and time (T) are taken as fundamental units, the dimensions of mass will be

1. [FvT^-1]

2. [FvT^-2]

3. [Fv^-1T^-1]

4. [Fv^-1T]

The dimensions of ${\left({\mu }_0{\epsilon }_0\right)}^{-1/2}$ are -

1.  $[ L^{-1}T ]$

2.  $[ L{T}^{-1} ]$

3.  $[ L^{1/2}{T}^{1/2} ]$

4. $[ L^{1/2}{T}^{-1/2} ]$

The dimensions of ${\left({\mathrm{\mu }}_0{\mathrm{\epsilon }}_0\right)}^{-1/2}$ are

1.  $\left[{\mathrm{L}}^{-1} \mathrm{T}\right]$

2.  $\left[{\mathrm{LT}}^{-1}\right]$

3.  $\left[{\mathrm{L}}^{-1/2} {\mathrm{T}}^{1/2}\right]$

4.  $\left[{\mathrm{L}}^{-1/2} {\mathrm{T}}^{-1/2}\right]$

The density of a material in CGS system of units is 4 g/cm³. In a system of units in which unit of length is 10 cm and unit of mass is 100g, the value of density of material will be
1. 0.04
2. 0.4
3. 40
4. 400

The dimensions of $\frac{1}{2}{\mathrm{\epsilon }}_0{\mathrm{E}}^2$ where ${\epsilon }_0$ is the permittivity of free space and E is the electric field, are:

1. [ML²T^-2]

2. [ML^-1T^-2]

3.  [ML²T^-1]

4.  [MLT^-1]

A student measures the distance traversed in free fall of a body, initially at rest in a given time. He uses this data to estimate g, the accelration due to gravity. If the maximum percentage errors in measurement of the distance and the time are e₁
and e₂ respectively, the percentage error in the estimation of g is -

1. $e_1+2e_2$

2. $e_1+e_2$

3. $e_1-2e_2$

4. $e_2-e_1$