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 density of material in the 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 when the value of density of material in this system will be:

(1) 0.4

(2) 40

(3) 400

(4) 0.04 

The dimension of $\frac{1}{2}{\epsilon }_0{E}^2,$ where ${\epsilon }_0$ is permittivity of free space and E is electric field, is

(a) $\left[M{L}^2{T}^{-2}\right]$                                   (b) $\left[M{L}^{-1}{T}^{-2}\right]$

(c) $\left[M{L}^2{T}^{-1}\right]$                                   (d) $\left[ML{T}^{-1}\right]$

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 dimension of a physical quantity are given by ${\mathrm{M}}^{\mathrm{a}}{\mathrm{L}}^{\mathrm{b}}{\mathrm{T}}^{\mathrm{c}},$ then the physical quantity will be

1. pressure if a=1, b=-1, c=-2

2. velocity if a=1, b=0, c=-1

3. acceleration if a=1, b=1,c=-2

4. force if a=0, b=-1, c=-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:

1. 4%                                                   2. 6%

3. 8%                                                   4. 2%

Which two of the following five physical parameters have the same dimensions ?

(1) energy density 

(2) refractive index 

(3) dielectric constant 

(4) Young's modulus 

(5) magnetic field 

1. 2 and 4

2. 3 and 5 

3. 1 and 4 

4. 1 and 5

Consider the following equation of Bernoulli’s theorem-

$\mathrm{P}+\frac{1}{2}{\mathrm{\rho V}}^2+\mathrm{\rho gh}=\mathrm{K}\left(\mathrm{constant}\right)$

The dimensions of K/P are the same as that of which of the following?

1. Thrust                         

2. Pressure

3. Angle                         

4. Viscosity

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

(1) [FvT^-1]

(2) [FvT^-2]

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

(4) [Fv^-1T]

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 coefficient of viscosity of the liquid, the 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