physics probs?

Question

1-can a quantity have constant value and be dimensionless?

2-convert a power of one mega watt on a system whose fundamental units are 10kg,1dm and i minute.

3-the height of mercury column in a barometer in a calcutta laboratory was recorded to be 75cm.calculate this pressure in SI and c.g.s units using the following data:specific gravity of mercury=13.6,density of water-1000kg/m^3,g=9.8m/sec^2 at calcutta.pressure=h rho g in usual symbols?

4-the dimensions of sigma b^4 (where sigma is stefan's constant and b is wien's consatnt) are [ml^4t^-3].is it true?

5-the velocity v of a particle depends upon time t,according to the equation v=a+bt+c/d+t.write the dimension of a,b,c and d.

6-dimension of young modulus?

7-calculate the dimensions of linear momentum and surafce tension in terms of velocity v,density rho,and frequency as fundamental units.

8-find the value of 60 joule/min on a system which has 100 g,100cm and i min as fundamental units.

Answer 1

1-can a quantity have constant value and be dimensionless?
Certain quantities are defined as the ratio of two quantities of the same kind, and are thus dimensionless, or have a dimension that may be expressed by the number one. The coherent SI unit of all such dimensionless quantities, or quantities of dimension one, is the number one, since the unit must be the ratio of two identical SI units. The values of all such quantities are simply expressed as numbers, and the unit one is not explicitly shown. Examples of such quantities are refractive index, relative permeability, and friction factor. There are also some quantities that are defined as a more complex product of simpler quantities in such a way that the product is dimensionless. Examples include the "characteristic numbers" like the Reynolds number Re = L/, where is mass density, is dynamic viscosity, is speed, and L is length. For all these cases the unit may be considered as the number one, which is a dimensionless derived unit.

Another class of dimensionless quantities are numbers that represent a count, such as a number of molecules, degeneracy (number of energy levels), and partition function in statistical thermodynamics (number of thermally accessible states). All of these counting quantities are also described as being dimensionless, or of dimension one, and are taken to have the SI unit one, although the unit of counting quantities cannot be described as a derived unit expressed in terms of the base units of the SI. For such quantities, the unit one may instead be regarded as a further base unit.

In a few cases, however, a special name is given to the unit one, in order to facilitate the identification of the quantity involved. This is the case for the radian and the steradian. The radian and steradian have been identified by the CGPM as special names for the coherent derived unit one, to be used to express values of plane angle and solid angle, respectively, and are therefore included in Table 3.

Some quantities have no dimensions. For example, the sine of an angle is defined as the ratio of the lengths of two particular sides of a triangle. Thus, the dimensions of the sine are L/L, or 1. Therefore, the sine function is said to be "dimensionless". There are many other examples of "dimensionless" quantities listed in the following table.
all trigonometric functions
exponential functions
logarithms
angles (but notice the discussion in the next paragraph)
quantities which are simply counted, such as the number of people in the room
plain old numbers (like 2, p, etc.)


2-convert a power of one mega watt on a system whose fundamental units are 10kg,1dm and i minute.
1 mega waat=10^6 waats
=10^6 joules/second
=10^6newtonmeter/second
=10^6kg*ms^-2/second
=10^6kgmetersec^-3
=10^6kg*10dm(1/60min)^-3

3-the height of mercury column in a barometer in a calcutta laboratory was recorded to be 75cm.calculate this pressure in SI and c.g.s units using the following data:specific gravity of mercury=13.6,density of water-1000kg/m^3,g=9.8m/sec^2 at calcutta.pressure=h rho g in usual symbols?
pressure=h*d*g
=0.75*13.6*10^3*9.8 Pascals in S.I.Units
=75*13.6*980 C.G.S.units

4-the dimensions of sigma b^4 (where sigma is stefan's constant and b is wien's consatnt) are [ml^4t^-3].is it true?
sigma=5.67 X 10-8 W/m2K-4
wiens constant=W = 2897 mK


5-the velocity v of a particle depends upon time t,according to the equation v=a+bt+c/d+t.write the dimension of a,b,c and d.

6-dimension of young modulus?
force/length^2

7-calculate the dimensions of linear momentum and surafce tension in terms of velocity v,density rho,and frequency as fundamental units.
linear momentum=MLT^-1

8-find the value of 60 joule/min on a system which has 100 g,100cm and i min as fundamental units.
60 joules=60MLT^-2/T=60MLT^-3
60(100)g*(100)cm*(1)min^-3

Answer 2

Scalar quantaties are things like money, mass, etc. So yep, they can be dimensionless!!

5. a, b, c should all be in metres and d in seconds.

really can't be bothered doing the rest. sorry i'm busy lol.

Answer 3

How can a scalar quantity be dimensionless?

Answer 4

1 - yes, a scalar quantity, such as a vector's magnitude.

..... don't have enough time to answer the other's

Answer 5

I really appreciate Raj's patience in answering this question.but i feel you havent given this question its due.I guess this is your assignment and translating that to yahoo answers is not a fair thing to do.