Choose any one of the following four responses :

Assertion : The quantity $(1\text{}/\text{}\sqrt{{\mu }_0{\epsilon }_0})$ is dimensionally equal to velocity and numerically equal to velocity of light.

Reason : ${\mu }_0$ is permeability of free space and ${\epsilon }_0$ is the permittivity of free space.

The surface tension of a liquid is 70 dyne/cm. In MKS system its value is 

The SI unit of universal gas constant (R) is

The unit of permittivity of free space ${\epsilon }_0$ is

What are the units of $K=1\text{}/\text{}4\pi {\epsilon }_0$

The SI unit of surface tension is

E, m, l and G denote energy, mass, angular momentum and gravitational constant respectively, then the dimension of $\frac{E{l}^2}{m^5{G}^2}$ are

One astronomical unit is a distance equal to 

Ampere second is a unit of 

A dimensionally consistent relation for the volume V of a liquid of coefficient of viscosity η flowing per second through a tube of radius r and length l and having a pressure difference p across its end, is

The velocity v (in cm/sec) of a particle is given in terms of time t (in sec) by the relation $v=at+\frac{b}{t+c}$; the dimensions of a, b and c are

From the dimensional consideration, which of the following equation is correct ?

The position of a particle at time t is given by the relation $l =\frac{v_o}{\alpha }(1-e^{\alpha t})$ , where v₀ is a constant and α > 0. The dimensions of v₀ and α are respectively

The dimensions of $\frac{a}{b}$ in the equation $P=\frac{a-t^2}{bx}$, where P is pressure, x is distance and t is time, are 

Dimensions of $\frac{1}{{\mu }_0{\epsilon }_0}$, where symbols have their usual meaning, are 

The dimensions of $e^2/4\pi {\epsilon }_{0}hc$, where $e,{\epsilon }_0,h$ and c are electronic charge, electric permittivity, Planck’s constant and velocity of light in vacuum respectively 

If radius of the sphere is (5.3 ± 0.1)cm. Then percentage error in its volume will be 

The pressure on a square plate is measured by measuring the force on the plate and the length of the sides of the plate. If the maximum error in the measurement of force and length are respectively 4% and 2%. The maximum error in the measurement of pressure is 

While measuring the acceleration due to gravity by a simple pendulum, a student makes a positive error of 1% in the length of the pendulum and a negative error of 3% in the value of time period. His percentage error in the measurement of g by the relation $g=4{\pi }^2(l/T^2)$ will be

The length, breadth, and thickness of a block are given by l = 12 cm, b = 6 cm and t = 2.45 cm The volume of the block according to the idea of significant figures should be:

A physical quantity of the dimensions of length that can be formed out of c, G and $\frac{e^2}{4\pi {\epsilon }_o}$ is [c is the velocity of light, G is the universal constant of gravitation and e is charge]

(a) $\frac{1}{c^2}{\left[G\frac{e^2}{4\pi {\epsilon }_o}\right]}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$

(b) $c^2{\left[G\frac{e^2}{4\pi {\epsilon }_o}\right]}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$

(c) $\frac{1}{c^2}{\left[\frac{e^2}{G4\pi {\epsilon }_o}\right]}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$

(d) $\frac{1}{c}G\frac{e^2}{4\pi {\epsilon }_0}$

Planck's constant (h),speed of light in vacuum (c) and Newton's gravitational constant (G) are three fundamental constants. Which of the following combinations of these has the dimensions of length?

If energy (E), velocity (v) and time (T) are chosen as the fundamental quantities, the dimensional formula of surface tension will be
 

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

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

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

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:

Which of the following is a units that of force?

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