Dimensions & Dimensional Analysis: JEE Questions & Solutions

Consider a modified Bernoulli equation. P + A/Bt² + ρ g(h + Bt) + 1/2 ρ v² = constant If t has the dimension of time then the dimensions of…

Match the LIST-I with LIST-II List-I List-II A. Spring constant I. ML²T⁻²K⁻¹ B. Thermal conductivity II. ML⁰T⁻² C. Boltzmann constant III.…

A ball of radius r and density ρ dropped through a viscous liquid of density σ and viscosity η attains its terminal velocity at time t,…

Match the LIST-I with LIST-II: List-I List-II A. Magnetic induction I. M L T⁻² A⁻² B. Magnetic flux II. M L² T⁻² A⁻² C. Magnetic…

Match List–I with List–II. List–I & List–II A. Coefficient of viscosity & I. [ML⁻¹T⁻²] B. Surface tension & II. [ML⁻²T⁻²] C. Pressure &…

If B is magnetic field and μ₀ is permeability of free space, then the dimensions of B/μ₀ is:

Which one of the following is the correct dimensional formula for the capacitance in F? M, L, T, and C stand for unit of mass, length,…

The position of a particle moving on x-axis is given by x(t) = A sin t + B cos² t + Ct² + D, where t is time. The dimension of ABC/D is:

The electric flux is φ = α σ + β λ where λ and σ are linear and surface charge density, respectively, and ( α/β) represents

Match List-I with List-II. List-I List-II (A) Permeability of free space (I) [M L² T⁻²] (B) Magnetic field (II) [M T⁻² A⁻¹] (C) Magnetic…

The energy E and momentum p of a moving body of mass m are related by some equation. Given that c represents the speed of light, identify…

In a measurement, it is asked to find the modulus of elasticity per unit torque applied on the system. The measured quantity has the…

Match List - I with List - II. | List - I | List - II | |---|---| | (A) Angular Impulse | (I) [M⁰ L² T⁻²] | | (B) Latent Heat | (II) [M L²…

The pair of physical quantities not having same dimensions is:

Match List-I with List-II. | List-I | List-II | |---|---| | (A) Young's Modulus | (I) ML⁻¹T⁻¹ | | (B) Torque | (II) ML⁻¹T⁻² | | (C)…

Match List-I with List-II. | List-I | List-II | |---|---| | (A) Coefficient of viscosity | (I) [ML⁰T⁻³] | | (B) Intensity of wave | (II)…

Given a charge q, current I and permeability of vacuum μ₀. Which of the following quantity has the dimension of momentum?

If μ₀ and ε₀ are the permeability and permittivity of free space, respectively, then the dimension of ( 1/(μ₀ ε₀)) is:

Match the LIST-I with LIST-II LIST-I LIST-II A. Gravitational constant I. [LT⁻²] B. Gravitational potential energy II. [L²T⁻²] C.…

Match the LIST-I with LIST-II | LIST-I | LIST-II | | --- | --- | | A. Boltzmann constant | I. ML²T⁻¹ | | B. Coefficient of viscosity | II.…

In an electromagnetic system, the quantity representing the ratio of electric flux and magnetic flux has dimension of M^P L^Q T^R A^S,…

In an electromagnetic system, a quantity defined as the ratio of electric dipole moment and magnetic dipole moment has dimensions of [M^P…

The dimension of √(μ₀/ε₀) is equal to that of: (Where μ₀ is the vacuum permeability and ε₀ is the vacuum permittivity)

Match List-I with List-II. | List-I | List-II | | --- | --- | | (A) Mass density | (I) [ML²T⁻³] | | (B) Impulse | (II) [MLT⁻¹] | | (C)…

The equation of state of a real gas is given by ( P + a/V²)(V - b) = RT, where P, V, and T are pressure, volume, and temperature. The…

Match List-I with List-II. | List-I | List-II | |---|---| | (A) Coefficient of viscosity | (I) [ML²T⁻²] | | (B) Surface tension | (II)…

If mass is written as m = k c^p G^(-1/2) h^(1/2), then the value of p will be:

A force is represented by F = ax² + bt^(1/2) where x = distance and t = time. The dimensions of b²/a are:

The de-Broglie wavelength associated with a particle of mass m and energy E is: λ = h/√2mE The dimensional formula for Planck’s constant is:

Match List I with List II: List I A. Planck's constant h B. Stopping potential V_s C. Work function Φ D. Momentum p List II I. M¹L²T⁻² II.…

The frequency (ν) of an oscillating liquid drop may depend upon radius (r) of the drop, density (ρ) of liquid and the surface tension (s)…

Match List I with List II: | List I | List II | |---|---| | (A) Surface tension | (I) kg m⁻¹ s⁻¹ | | (B) Pressure | (II) kg m s⁻¹ | | (C)…

Match List I with List II | List I | List II | |---|---| | (A) Young's Modulus (Y) | (I) [M L⁻¹ T⁻¹] | | (B) Co-efficient of Viscosity (η)…

Match List-I with List-II: | List-I (Physical Quantity) | List-II (Dimensional Formula) | |---|---| | (A) Pressure gradient | (I) [M⁰L²T⁻²]…

The equation of a circle is given by x² + y² = a², where a is the radius. If the equation is modified to change the origin other than ((0,…

Match List I with List II | List I | List II | |---|---| | (A) Torque | (I) kg m⁻¹ s⁻² | | (B) Energy density | (II) kg m s⁻¹ | | (C)…

If R, X_L, and X_C represent resistance, inductive reactance, and capacitive reactance, then which of the following is dimensionless:

Match List-I with List-II. List-I List-II A. Angular momentum I. [ML²T⁻²] B. Torque II. [ML⁻²T⁻²] C. Stress III. [ML²T⁻¹] D. Pressure…

The equation of state for some gases is given by: ( P + a/V²) (V - b) = RT The physical quantity, which has the same dimensional formula as…

If the velocity of light c, universal gravitational constant G and Planck's constant h are chosen as fundamental quantities. The dimensions…

Dimension of 1/(μ₀ ε₀) should be equal to:

If force (F), velocity (V) and time (T) are considered as fundamental physical quantity, then dimensional formula of density will be:-

Match List I with List II | List I | List II | |---|---| | (A) Spring constant | (I) [T⁻¹] | | (B) Angular speed | (II) [MT⁻²] | | (C)…

The speed of a wave produced in water is given by v=λ^a g^b ρ^c, where λ, g and ρ are the wavelength of the wave, acceleration due to…