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QUESTION: 1

The pairs of physical quantities that have the same dimensions are

Solution:

Reynold's number and coefficient of friction are dimensionless quantities. Curie is the number of atoms decaying per unit time and frequency is the number of oscillations per unit time. Latent heat and gravitational potential both have the same dimension corresponding to energy per unit mass.

*Multiple options can be correct

QUESTION: 2

In the formula X = 3YZ^{2}, X and Z have dimensions of capacitance and magnetic induction respectively. What are the dimensions of Y in MKSQ system ?

[JEE-1995,2/100]

Solution:

*Multiple options can be correct

QUESTION: 3

Which of the following pairs have same dimensions :

[JEE-1996' 2/100]

Solution:

Torque = Work = Energy =[ML^{2}T^{-2}]

Angular momentum =mvr=[ML^{2}T^{-1}]

Young's modulus =[ML^{-1}T^{-2}]

Light year and wavelength= [M^{0}L^{1}T^{0}]

A and C have the same dimension.

QUESTION: 4

The respective number of significant figures for the numbers 23.023, 0.0003 and 2.1 × 10^{–3} are

Solution:

(i) All the non-zero digits are significant.

(ii) All the zeros between two non-zero digits are significant, no matter where the decimal point is, if at all.

(iii) If the number is less than 1, the zero(s) on the right of decimal point but to the left of the first non-zero digit are not significant.

(iv) The power of 10 is irrelevant to the determination of significant figures. According to the above rules, 23.023 has 5 significant figures. 0.0003 has 1 significant figures. 2.1 × 10^{–3} has 2 significant figures.

QUESTION: 5

Let [ε_{0}] denote the dimensional formula of the permittivity of the vaccum, and [μ_{0}] that of the permeability of the vacuum. If M = mass, L = length, T = time and I = electric current :

[JEE-1998' 2/200]

Solution:

QUESTION: 6

A dense collection of equal number of electrons and positive ions is called neutral plasma. Certain solids containing fixed positive ions surrounded by free electrons can be treated as neutral plasma. Let 'N' be the number density of free electrons, each of mass 'm'. When the electrons are subjected to an electric field, they are displaced relatively away from the heavy positive ions. If the electric field becomes zero, the electrons begin to oscillate about the positive ions with a natural angular frequency 'wP' which is called the plasma frequency. To sustain the oscillations, a time varying electric field needs to be applied that has an angular frequency w, where a part of the energy is absorbed and a part of it is reflected. As w approaches wP, all the free electrons are set to resonance together and all the energy is reflected. This is the explanation of high reflectivity of metals.

Taking the electronic charge as 'e' and the permittivity as 'ε0', use dimensional analysis to determine the correct expression for wP.

Solution:

Dimension of N = [L - 3]

QUESTION: 7

A quantity X is given by ε_{0}L . where ε_{0} is the permittivity of free space, L is length, ΔV is potential difference and Δt is time interval. The dimensional formula for X is the same as that of

[JEE Sc.2000'3/105]

Solution:

QUESTION: 8

Pressure depends on distance as, P = , where α, β are constants, z is distance, k is Boltzmann's constant and q is temperature. The dimension of β are

[JEE-2004s '3/84]

Solution:

Unit of K is joules per kelvin or the dimensional formula of Kis [ML^{2}T^{-2}θ^{-1}].

αz/kθ should be dimensionless,

So, dimensional formula of α = [ML^{2}T^{-2}]/[L] = MLT^{-2}

Dimensional formula of P = [ML^{-1}T^{-2}]

rArr β = [α/P]

= [MLT^{-2}]/[ML^{-1}T^{-2}]

= M^{0}L^{2}T^{0}

*Multiple options can be correct

QUESTION: 9

Which of the following set have different dimensions ?

[JEE-2005s ; 3/60]

Solution:

By checking dimension all option

[Dipole moment] = [M^{0}L^{1}T^{1}A^{1}] [Electric Flux] = [M^{1}L^{3}T^{-3}I^{-1}] [Electric field] = [M^{1}L^{1}T^{-3}I^{-}^{1}]

*Answer can only contain numeric values

QUESTION: 10

What is the percentage error in the physical quantity A If it is related to four other physical quantities a,b, c and d as The percentage error in measurement of a,b,c and d are 1% , 3% 2% and 1% respectively

Solution:

Percentage error of A

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