Dimensions

The velocity of a particle at time is given by , where and are constants. The dimensions of and are respectively:
1.
2.
3.
4.

Dimensions of resistance in an electrical circuit, in terms of dimension of mass M, length L, time T, and current I, would be:

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

2. $\left[{\mathrm{ML}}^2{\mathrm{T}}^{-2}\right]$

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

4. $\left[{\mathrm{ML}}^2{\mathrm{T}}^{-3}{\mathrm{I}}^{-2}\right]$

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]

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

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

2. $\left[{\mathrm{LT}}^{-1}\right]$

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

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

If dimensions of critical velocity of a liquid flowing through a tube are expressed as , where are the coefficient of viscosity of the liquid, the density of the liquid, and the radius of the tube respectively, then the values of and respectively, will be:

1.		2.
3.		4.

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

1.		2.
3.		4.

A physical quantity of the dimensions of length that can be formed out of is:
( is the velocity of light, is the universal constant of gravitation and is charge)

1.		2.
3.		4.

The unit of thermal conductivity is:

1.	W m–1 K–1	2.	J m K–1
3.	J m–1 K–1	4.	W m K–1

If force , acceleration and time are chosen as the fundamental physical quantities, then find the dimensions of energy:

1.		2.
3.		4.

If and respectively, denote energy and gravitational constant, then has the dimensions of:
1.
2.
3.
4.

Plane angle and solid angle have:

1.	both units and dimensions
2.	units but no dimensions
3.	dimensions but no units
4.	no units and no dimensions

The dimensions belong to the:
1. electric permittivity
2. magnetic flux
3. self-inductance
4. magnetic permeability

The quantities which have the same dimensions as those of solid angle are:
1. stress and angle
2. strain and arc
3. angular speed and stress
4. strain and angle

A force defined by; acts on a particle at a given time The factor which is dimensionless, if and are constants, is:

1.		2.
3.		4.

A balloon is made of a material of surface tension and its inflation outlet (from where gas is filled in it) has small area It is filled with a gas of density and takes a spherical shape of radius When the gas is allowed to flow freely out of it, its radius changes from to (zero) in time If the speed of gas coming out of the balloon depends on as and then:

1.
2.
3.
4.