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प्रश्न
Give an example of a physical quantity which has a unit but no dimensions.
उत्तर
Solid angle Ω = `A/r^2` steradian and a plane angle θ = `L/r` radian. Both are dimensionless but have units.
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संबंधित प्रश्न
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.
Explain this common observation clearly : If you look out of the window of a fast moving train, the nearby trees, houses, etc. seem to move rapidly in a direction opposite to the train’s motion, but the distant objects (hill tops, the Moon, the stars etc.) seem to be stationary. (In fact, since you are aware that you are moving, these distant objects seem to move with you).
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)`
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
Why length, mass and time are chosen as base quantities in mechanics?
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 ______.
P = `alpha/beta` exp `(-"az"/"K"_"B"theta)`
θ `→` Temperature
P `→` Pressure
KB `→` Boltzmann constant
z `→` Distance
Dimension of β is ______.
