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.
The unit of length convenient on the atomic scale is known as an angstrom and is denoted by Å : 1Å = 10−10 m. The size of a hydrogen atom is about 0.5 Å. What is the total atomic volume in m3 of a mole of hydrogen atoms?
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):
If area (A), velocity (V) and density (p) are taken as fundamental units, what is the dimensional formula for force?
A function f(θ) is defined as: `f(θ) = 1 - θ + θ^2/(2!) - θ^3/(3!) + θ^4/(4!)` Why is it necessary for q to be a dimensionless quantity?
Why length, mass and time are chosen as base quantities in mechanics?
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.
In the expression P = E l2 m–5 G–2, E, m, l and G denote energy, mass, angular momentum and gravitational constant, respectively. Show that P is a dimensionless quantity.
If velocity of light c, Planck’s constant h and gravitational contant G are taken as fundamental quantities then express mass, length and time in terms of dimensions of these quantities.
An artificial satellite is revolving around a planet of mass M and radius R, in a circular orbit of radius r. From Kepler’s Third law about the period of a satellite around a common central body, square of the period of revolution T is proportional to the cube of the radius of the orbit r. Show using dimensional analysis, that `T = k/R sqrt(r^3/g)`. where k is a dimensionless constant and g is acceleration due to gravity.
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 ______.
