Advertisements
Advertisements
प्रश्न
If P, Q, R are physical quantities, having different dimensions, which of the following combinations can never be a meaningful quantity?
- (P – Q)/R
- PQ – R
- PQ/R
- (PR – Q2)/R
- (R + Q)/P
Advertisements
उत्तर
a. (P – Q)/R
e. (R + Q)/P
Explanation:
Principle of Homogeneity of dimensions: It states that in a correct equation, the dimensions of each term added or subtracted must be the same. Every correct equation must have the same dimensions on both sides of the equation.
According to the problem P, Q and R are having different dimensions, since, the sum and difference of physical dimensions, are meaningless, i.e., (P – Q) and (R + Q) are not meaningful.
So in option (b) and (c), PQ may have the same dimensions as those of R and in options (d) PR and Q2 may have the same dimensions as those of R.
Hence, they cannot be added or subtracted, so we can say that (a) and (e) is not meaningful.
APPEARS IN
संबंधित प्रश्न
A calorie is a unit of heat or energy and it equals about 4.2 J where 1J = 1 kg m2s–2. Suppose we employ a system of units in which the unit of mass equals α kg, the unit of length equals β m, the unit of time is γ s. Show that a calorie has a magnitude 4.2 α–1 β–2 γ2 in terms of the new units.
A book with many printing errors contains four different formulas for the displacement y of a particle undergoing a certain periodic motion:
(a) y = a sin `(2pit)/T`
(b) y = a sin vt
(c) y = `(a/T) sin t/a`
d) y = `(a/sqrt2) (sin 2πt / T + cos 2πt / T )`
(a = maximum displacement of the particle, v = speed of the particle. T = time-period of motion). Rule out the wrong formulas on dimensional grounds.
A physical quantity of the dimensions of length that can be formed out of c, G and `e^2/(4piε_0)` is (c is velocity of light, G is universal constant of gravitation and e is charge):
The dimensional formula for latent heat is ______.
If area (A), velocity (V) and density (p) are taken as fundamental units, what is the dimensional formula for force?
On the basis of dimensions, decide which of the following relations for the displacement of a particle undergoing simple harmonic motion is not correct ______.
- y = `a sin (2πt)/T`
- y = `a sin vt`
- y = `a/T sin (t/a)`
- y = `asqrt(2) (sin (2pit)/T - cos (2pit)/T)`
Give an example of a physical quantity which has neither unit nor dimensions.
The volume of a liquid flowing out per second of a pipe of length l and radius r is written by a student as `v = π/8 (pr^4)/(ηl)` where P is the pressure difference between the two ends of the pipe and η is coefficient of viscosity of the liquid having dimensional formula ML–1 T–1. Check whether the equation is dimensionally correct.
Einstein’s mass-energy relation emerging out of his famous theory of relativity relates mass (m ) to energy (E ) as E = mc2, where c is speed of light in vacuum. At the nuclear level, the magnitudes of energy are very small. The energy at nuclear level is usually measured in MeV, where 1 MeV= 1.6 × 10–13 J; the masses are measured in unified atomic mass unit (u) where 1u = 1.67 × 10–27 kg.
- Show that the energy equivalent of 1 u is 931.5 MeV.
- A student writes the relation as 1 u = 931.5 MeV. The teacher points out that the relation is dimensionally incorrect. Write the correct relation.
The entropy of any system is given by `S = alpha^2betaIn[(mukR)/(Jbeta^2) + 3]` Where α and β are the constants µ J, k, and R are no. of moles, the mechanical equivalent of heat, Boltzmann constant, and gas constant respectively. `["take S" = (dQ)/T]`
Choose the incorrect option from the following.
The workdone by a gas molecule in an x' isolated system is given by, W = αβ2 `e^(-x^2/(alpha"KT"))`, where x is the displacement, k is the Boltzmann constant and T is the temperature. α and β are constants. Then the dimensions of β will be ______.
A wave is represented by y = a sin(At - Bx + C) where A, B, C are constants and t is in seconds and x is in metre. The Dimensions of A, B, and C are ______.
P = `alpha/beta` exp `(-"az"/"K"_"B"theta)`
θ `→` Temperature
P `→` Pressure
KB `→` Boltzmann constant
z `→` Distance
Dimension of β is ______.
The quantities which have the same dimensions as those of solid angle are ______.
A force defined by F = αt2 + βt acts on a particle at a given time t. The factor which is dimensionless, if α and β are constants, is ______.
