Advertisements
Advertisements
Question
Give an example of a physical quantity which has a unit but no dimensions.
Advertisements
Solution
Solid angle Ω = `A/r^2` steradian and a plane angle θ = `L/r` radian. Both are dimensionless but have units.
APPEARS IN
RELATED QUESTIONS
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.
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):
The dimensional formula for latent heat is ______.
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.
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 ______.
