If energy (E), velocity (V) and time (T) are chosen as the fundamental quantities, the dimensional formula of surface tension will be :
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(b) Let surface tension
Equating the dimension of LHS and RHS
Hence, the dimensions of surface tension are
If dimensions of critical velocity of a liquid flowing through a tube are expressed as , where and are the coefficient of viscosity of liquid, density of liquid and radius of the tube respectively, then the values of and are given by :
(d) Applying dimensional method :
Equating powers both sides
Planck's constant , speed of light in vacuum (c) and Newton's gravitational constant are three fundamental constants. Which of the following combinations of these has the dimension of length?
A physical quantity of the dimensions of length that can be formed out of and is [ is velocity of light, is universal constant of gravitation and is charge]
(d) Let dimensions of length is related as,
Comparing both sides
From (i), (ii) & (iii)
Hence,
In an experiment, the percentage of error occurred in the measurement of physical quantities an are , and respectively. Then the maximum percentage of error in the measurement , where will be :
(b) Given,
error,
The unit of thermal conductivity is :
(d) In steady state, the amount of heat flowing from one face to the other face in time is given by
coefficient of thermal conductivity
Unit of
Dimensions of stress are :
(c) Stress
Dimension of force
Dimension of area
Stress
Taking into account of the significant figures, what is the value of ?
(a) In subtraction the number of decimal places in the result should be equal to the number of decimal places of that term in the operation which contain lesser number of decimal places. 9.99
As the least number of decimal places is 3 . So, answer should be .
If and respectively denote energy and gravitational constant, then has the dimensions of
Dimensional formula of energy
Dimensional formula of gravitational constant
From eq. (i) & (ii)
Numerical constant like, or has no dimension.
If force , acceleration and time are chosen as the fundamental physical.quantities. Find the dimensions of energy
Energy,
Comparing dimensions on both sides.
and
and or,
Dimensions of energy
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