# Dimensional Analysis

## Trending Questions

**Q.**

The frequency of vibration of a string depends on the length L between the nodes, the tension F in the string and its mass per unit length m, Guess the expression for its frequency from dimensional analysis.

**Q.**

What is the dimensional formula of epsilon not?

**Q.**Planck’s constant (h), speed of light in vacuum (c) and Newton’s gravitational constant (G) are three fundamental constants. Which one of the following combinations of these has the dimension of length?

- √hGC3
- √hGC5/2
- √hCG
- √GCh3/2

**Q.**A charge Q is fixed at each of two opposite corners of a square. A charge q is placed at each of the other two corners. If the resultant electric force on Q is zero, then Q and q are related as

- Q=√2q
- Q=−2√2q
- Q=Q=−√2q
- Q=2√2q

**Q.**If dimensions of critical velocity vc of a liquid flowing through a tube are expressed as [ηxρyrz], where η, ρ and r are the coefficient of viscosity of liquid, density of liquid and radius of the tube respectively, then values of x, y and z are given by

- 1, -1, -1
- 1, 1, 1

-1, -1, 1- -1, -1, -1

**Q.**

Assuming that the mass M of the largest stone that can be moved by flowing river depends on the velocity of water V density of water p and the acceleration due to gravity G then M is directly proportional to

**Q.**The equation of a wave is given by

y=Asinω(xv−a), where ω is the angular velocity and v is the linear velocity of the wave. The dimensions of a is

- [M]
- [T]
- [L]
- [K]

**Q.**

If speed V, area A, and force F are chosen as fundamental units then the dimension of Youngâ€™s modulus will be:

$F{A}^{2}{V}^{-3}$

$F{A}^{2}{V}^{-2}$

$F{A}^{-1}{V}^{0}$

$F{A}^{2}{V}^{-1}$

**Q.**Consider the region of electric field, as shown in the figure. Work done by the electric field, in carrying a protonfrom point B to point A, will be4.VA 10 VVB 20 V(1) 1.610-18J(3) 1.6 x 10-19 J(2)(4)-1.610-18J-1.6 x 10-19 Jsh Educational Saricoo Lt

**Q.**The given figure shows a set of equipotential surfaces. Find the magnitude and direction of electric field that exists in the region.

**Q.**

A cube of side L is placed in a uniform electric field, â†’E=E Ë†i. The net electric flux through the cube is

- 0
- L2E
- 4L2E
- 6L2E

**Q.**

Find the dimension formula for resistance.

**Q.**If time (t), velocity (v), and angular momentum (l) are taken as the fundamental units. Then the dimension of mass (m) in terms of t, v and l is :

- [t−2v−1l1]
- [t−1v1l−2]
- [t−1v−2l1]
- [t1v2l−1]

**Q.**What is the SI unit of surface tension?

**Q.**What is the dimensional formula for permittivity of free space?

- [M−1L−3T0A2]
- [M−1L3T0A2]
- [M−1L−3T4A2]
- [M−1L−3T4]

**Q.**The equation of the stationary wave is

y=2Asin(2πctλ)cos(2πxλ)

Which of the following statements is wrong?

- The unit of ct is same as that of λ
- The unit of x is same as that of λ
- The unit of 2πcλ is same as that of 2πxλt
- The unit of cλ is same as that of xλ

**Q.**

What is the SI unit of mechanical equivalent of heat?

**Q.**Define power.

**Q.**In a series resonant LCR circuit, the voltage across resistor R is 100 V and R=1 kΩ with C=2 μF. The resonant frequency ω is 200 rad/s. At resonance, the voltage across L is

- 2.5×10−2 V
- 40 V
- 250 V
- 4×10−3 V

**Q.**In C.G.S. system the magnitude of the force is 100 dynes. In another system where the fundamental physical quantities are kilogram, metre and minute, the magnitude of the force is

- 3.6
- 36
- 0.036
- 0.36

**Q.**A particle executes simple harmonic motion with an amplitude of 5 cm. When the particle is at 4 cm from the mean position, the magnitude of its velocity in SI units is equal to that of its acceleration. Then, its periodic time in seconds is

- 4π3
- 38π
- 8π3
- 73π

**Q.**If force (F), velocity (V) and time (T) are taken as fundamental units, then dimensions of mass are

- [FVT−1]
- [FV−1T−1]
- [FVT−2]
- [FV−1T]

**Q.**

What is the dimensional formula for thermal resistance?

**Q.**

A student performs experiment with simple pendulum and measures time for 10 vibrations . If he measures time for 100 vibrations , the relative error in measurements of time period will be reduced by

**Q.**The unit of plane angle is radian, hence its dimensions are

- [M0L0T0]
- [M1L−1T0]
- [M1L0T−1]
- [M0L1T−1]

**Q.**In the ideal gas equation PV=nRT, dimensional formula of R is

- [ML2T−2K−1mol−1]
- [ML2Kmol]
- [L2T−1K−1mol]
- [M2L2T−2K−2mol−1]

**Q.**The electric field in a region is given by →E=(Ax+B)^i, where E is in NC−1 and x is in metres. The values of constants are A=20 SI unit and B=10 SI unit. If the potential at x=1, is V1, and that at x=−5 is V2, then V1−V2

- −48 V
- 180 V
- 320 V
- −520 V

**Q.**If velocity V, acceleration A and force F are taken as fundamental quantities, then the dimensional formula of angular momentum in terms of V, A and F will be

- [FA−1V]
- [FA−2V3]
- [F2A−1V2]
- [FA−1V2]

**Q.**

A
long solenoid with 15 turns per cm has a small loop of area 2.0 cm^{2
}placed inside the solenoid normal
to its axis. If the current carried by the solenoid changes steadily
from 2.0 A to 4.0 A in 0.1 s, what is the induced emf in the loop
while the current is changing?

**Q.**

Which of the following is not a fundamental quantity?

Current

Time

Weight

Length