# Limitation of Dimensional Analysis

## Trending Questions

**Q.**A physical quantity x depends on quantities y and z as follows: x=Ay+B tan(Cz), where A, B and C are constants. Which of the following do not have the same dimensions?

- x and B
- x and A
- C and z−1
- y and B/A

**Q.**The time dependence of physical quantity P is found to be of the form P=Poe−αt2, where ‘t′ is the time and α is some constant. Then the constant α will

- be dimensionless
- have dimensions of T−2
- have dimensions of P
- have dimensions of P multiplied by T−2

**Q.**In a simple harmonic oscillation, what fraction of total mechanical energy is in the form of kinetic energy, when the particle is midway between mean and extreme position.

- 14
- 13
- 12
- 34

**Q.**The dimension of a in Van der Waals equation (P+an2V2)(V−nb)=nRT is

- [ML5T−2]
- [ML5T]
- [M−1L5T2]
- [ML−5T−1]

**Q.**The Van Der Waal’s equation of state for some gases can be expressed as: (P+aV2)(V−b)=RT Where P is the pressure, V is the molar volume and T is the absolute temperature of the given sample of gas and a, b and R are constants.

Which of the following does not have the same dimension formula as that of RT ?

- PV
- Pb
- aV2
- abV2

**Q.**

Define dimensional formula. Give uses of dimensional analysis. Write down the limitations.

**Q.**

Capillary tube is a very thin tube. If it is dipped in water, water rises upto height h=2Trρg, where r is the radius of tube, ρ is density, and g is acceleration due to gravity. Find dimensional formula of [T]

- MLT−1
- MT−2
- M−1T2
- MLT−2

**Q.**The potential energy of a particle varies with distance x as Ax1/2x2+B, where A and B are constants. The dimensional formula for A×B is

- M1L72T−2
- M1L112T−2
- M1L92T−2
- M1L52T−2

**Q.**

Mention any two limitations of dimensional analysis.

**Q.**The Van Der Waal’s equation of state for some gases can be expressed as: (P+aV2)(V−b)=RT Where P is the pressure, V is the molar volume and T is the absolute temperature of the given sample of gas and a, b and R are constants.

The dimensions of constant b are

- ML5T−2
- ML−1T−2
- L3
- L6

**Q.**Write important limitations of dimensional analysis.

**Q.**State any two limitations of dimensional analysis.

**Q.**A quantity x is given by x=IFv2WL4, in terms of moment of inertia I, force F, velocity v, work W and length L. The dimensional formula for x is the same as that of :

- planck’s constant
- force constant
- energy density
- coefficient of viscosity

**Q.**The relation P=αβe(−αzkθ), where p is pressure, z is distance, k is Bolzmann constant and θ is temperature. The dimensional formula of β will be

- [ML0T−1]
- [M0L2T−1]
- [M0L2T0]
- [ML2T]

**Q.**Answer the following:

Mention three limitations of dimensional analysis.

**Q.**

Test dimensionally if the equation v2=u2 + 2ax may be correct.

correct for sure

may be correct

wrong for sure

none of these

**Q.**

The force F is given in terms of time t and displacement x by the equation F = A cos Bx + C sin Dt. The dimensional formula of DB is

[M0L0T0]

[M0L0T−1]

[M0L−1T0]

[M0L1T−1]

**Q.**The Van Der Waal’s equation of state for some gases can be expressed as: (P+aV2)(V−b)=RT

Where P is the pressure, V is the molar volume and T is the absolute temperature of the given sample of gas and a, b and R are constants.

The dimensions of a are

- L3
- ML5T−2
- ML−1T−2
- L6

**Q.**A highly rigid cubical block A of small mass M and side L is fixed rigidly onto another cubical block B of the same dimensions and of modulus of rigidity η such that the lower face of A completely covers the upper face of B. The lower face of B is rigidly held on a horizontal surface. A small force F is applied perpendicular to one of the side faces of A. After the force is withdrawn block A executes small oscillations. The time period of which is given by

- 2π√LMη
- 2π√MηL
- 2π√MLη
- 2π√MηL

**Q.**Two very long co-axial cylinders of radius R and 2R carry current I in opposite directions. Then energy stored in cylindrical region of radius 4R of unit length is

- 38μ0 i2π

- μ0 i24 π ln (2)

- μ0 i24 π ln (4)

- zero

**Q.**

**Q.**The time dependence of physical quantity P is found to be of the form P=Poe−αt2, where ‘t′ is the time and α is some constant. Then the constant α will

- be dimensionless
- have dimensions of T−2
- have dimensions of P
- have dimensions of P multiplied by T−2

**Q.**

As the sir said that he will teach the extent version of dimensions analysis but there is no vedio about it

Please share the the information to me

**Q.**Assertion :The units of some physical quantities can be expressed as combination of the base units. Reason: We need only a limited number of units for expressing the derived physical quantities.

- Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
- Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
- Assertion is correct but Reason is incorrect
- Both Assertion and Reason are incorrect

**Q.**If the linear charge density of a cylinder is 4μCm−1 then electric field intensity at point 3.6cm from axis is.

- 2×106NC−1
- 12×107NC−1
- 4×105NC−1
- 8×107NC−1

**Q.**Taking the electronic charge as ‘e’ and the permittivity as ‘ε0′, use dimensional analysis to determine the correct expression for ωp

- √Nemε0
- √mε0Ne2
- √Ne2mε0
- √mε0Ne

**Q.**The time dependence of a physical quantity P is given by P=P0eα(−αt2), where α is a constant and t is time. The constant α

- Is a dimension less
- Has dimensions of P
- Has dimensions of T
- Has dimensions of T−2

**Q.**The relation P=αβe(−αzkθ), where p is pressure, z is distance, k is Bolzmann constant and θ is temperature. The dimensional formula of β will be

- [M0L2T−1]
- [ML2T]
- [ML0T−1]
- [M0L2T0]

**Q.**Which of the following equations cannot be deduced using dimensional analysis?

**Q.**Sir what is meant by dimensional analysis and its limitations .

Can I have a answer in easy language. Not understood any of the dimensional analysis ?