The meter is defined as the distance travelled by light in second. Why didn’t people choose some easier number such as second ? Why not 1 second?

What are the dimensions of:

A. volume of a cube of edge a,

B. volume of a sphere of radius a,

C. the ratio of the volume of a cube of edge a to the volume of a sphere of radius a?

Suppose you are told that the linear size of everything in the universe has been doubled overnight. Can you test this statement by measuring sizes with a meter stick? Can you test it by using the fact that the speed of light is a universal constant and has not changed? What will happen if all the clocks in the universe also start running at half the speed?

If all the terms in an equation have same units, is it necessary that they have same dimensions? If all the terms in an equation have same dimensions, is it necessary that they have same units?

If two quantities have same dimensions, do they represent same physical content?

It is desirable that the standards of units be easily available, invariable, indestructible and easily reproducible. If we use foot of a person as a standard unit of length, which of the above features are present and which are not?

Suggest a way to measure:

A. the thickness of a sheet of paper,

B. the distance between the sun and the moon.

Which of the following sets cannot enter into the list of fundamental quantities in any system of units?

A physical quantity is measured and the result is expressed as nu where u is the unit used and n is the numerical value. If the result is expressed in various units then

Suppose a quantity x can be dimensionally represented in terms of M, L and T, that is, [x] = M^a L^b T^c . The quantity mass

A dimensionless quantity

A unit-less quantity

The value of n is

The dimensions ML^-1 T^-2 may correspond to

Choose the correct statement(s):

Choose the correct statement(s):

Find the dimensions of

A. linear momentum,

B. frequency and

C. pressure

Find the dimensions of

A. angular speed ω,

B. angular acceleration α,

C. torque Γ and

D. moment of inertia I.

Some of the equations involving these quantities are

and

The symbols have standard meanings.

Find the dimensions of

A. electric field E,

B. magnetic field B and

C. magnetic permeability μ₀.

The relevant equations are

and

where F is force, q is charge υ is speed, I is current, and a is distance.

Find the dimensions of

A. electric dipole moment p and

B. magnetic dipole moment M.

The defining equations are p = q.d and M = IA;

where d is distance, A is area, q is charge and I is current.

Find the dimensions of Planck’s constant h from the equation

E = hv where E is the energy and v is the frequency.

Find the dimensions of

A. the specific heat capacity c,

B. the coefficient of linear expansion α and

C. the gas constant R.

Some of the equations involving these quantities are

and

Taking force, length and time to be the fundamental quantities find the dimensions of

A. density, B. pressure,

C. momentum and D. energy.

Suppose the acceleration due to gravity at a place is 10 m/s².

Find its value in cm/(minute)².

The average speed of a snail is 0.020 miles/hour and that of a

leopard is 70 miles/hour. Convert these speeds in SI units.

The height of mercury column in a barometer in a Calcutta

laboratory was recorded to be 75 cm. Calculate this pressure in SI

and CGS units using the following data: Specific gravity of mercury

= 136, Density of water = 10³ kg/m³, g = 9.8 m/s² at Calcutta.

Pressure = hρg in usual symbols.

Express the power of a 100-watt bulb in CGS unit.

The normal duration of I.Sc. Physics practical period in Indian

colleges are 100 minutes. Express this period in microcenturies. 1 microcentury = 10^-6 × 100 years. How many microcenturies did you sleep yesterday?

The surface tension of water is 72 dyne/cm. Convert it in SI unit.

The kinetic energy K of a rotating body depends on its moment

of inertia I and its angular speed ω. Assuming the relation to be K =

kI^a ω^b where k is a dimensionless constant, find a and b. Moment of

inertia of a sphere about its diameter is Mr².

Theory of relativity reveals that mass can be converted into

energy. The energy E so obtained is proportional to certain powers of

mass m and the speed c of light. Guess a relation among the

quantities using the method of dimensions.

Let I = current through a conductor, R = its resistance and V =

potential difference across its ends. According to Ohm’s law, product

of two of these quantities equals the third. Obtain Ohm’s law from

dimensional analysis. Dimensional formulae for R and V are ML²I^-2T³

and ML² T^-3 I^-1 respectively.

The frequency of vibration of a string depends on the length L

between the nodes, the tension F in the string and its mass per unit

length m. Guess the expression for its frequency from dimensional

analysis.

Test if the following equations are dimensionally correct:

A. B.

C. D.

where h = height, S = surface tension, ρ = density, P = pressure,

V = volume, η = coefficient of viscosity, v = frequency and I =

moment of inertia.

Let x and α stand for distance. Is dimensionally

correct?