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
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
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)`
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?
Give an example of a physical quantity which has neither unit nor dimensions.
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.
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.
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 ______.
