If the unit of force and length each be increased by four times, then the unit of energy is increased by 

(1) 16 times

(2) 8 times

(3) 2 times

(4) 4 times

If energy (\(E\)), velocity (\(v\)) and time (\(T\)) are chosen as the fundamental quantities, the dimensional formula of surface tension will be:
1. \( {\left[E v^{-2} T^{-1}\right]} \)
2. \( {\left[E v^{-1} T^{-2}\right]} \)
3. \( {\left[E v^{-2} T^{-2}\right]} \)
4. \({\left[E^{-2} v^{-1} T^{-3}\right]}\)

If dimensions of critical velocity v_c of a liquid flowing through a tube are expressed as [$\eta$^xρ^yr^z]  , where $\eta$, ρ and r are the coefficent of viscocity of liquid, density of liquid and radius of the tube respectively, then the values of x,y and z are given by

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, then the dimensions of mass are:

(a) [FvT^-1]

(b) [FvT^-2]

(c) [Fv^-1T^-1]

(d) [Fv^-1T]

In an experiment four quantities a, b, c and d are measured with percentage error 1%,2%,3% and 4% respectively. Quantity P is calculated as follows P=a³b²/cd %, Error in P is

1. 14%

2. 10%

3. 7%

4. 4%

The dimension of $({\mathrm{\mu }}_0{\mathrm{\epsilon }}_0{)}^{-1/2}$ 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 material in CGS system of units is $4g/c{m}^3.$ In a system of units in which unit of length is 10cm and unit of mass is 100g, then the value of density of material in this system will be-

(1)0.4

(2)40

(3)400

(4)0.04 

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 acceleration due to gravity. If the maximum percentage errors in measurement of the distance and the time are ${\mathrm{e}}_1$ and ${\mathrm{e}}_2$ respectively, the percentage error in the estimation of g is:

1. ${\mathrm{e}}_2-{\mathrm{e}}_1$                                                2. ${\mathrm{e}}_1+2{\mathrm{e}}_2$

3. ${\mathrm{e}}_1+{\mathrm{e}}_2$                                                4. ${\mathrm{e}}_1-2{\mathrm{e}}_2$

If the error in the measurement of the radius of a sphere is \(2\%\), then the error in the determination of the volume of the sphere will be: