Units and Measurement

Which two of the following five physical parameters have the same dimensions?

1) Energy density
2) refractive index
3) dielectric constant
4) Young's modulus
5) Magnetic field

• 2 and 4

• 3 and 5

• 1 and 4

• 1 and 4

Dimensions of resistance in an electrical circuit, in terms of the dimension of mass M, of length L, of time T and of current I, would be:

• [ML²T^-3I^-1]

• [ML²T^-2]

• [ML²T^-1I^-1]

• [ML²T^-1I^-1]

The velocity v of a particle at time t is given by  where a, b and c are constants, The dimensions of a, b and c are respectively:

The physical quantity of the dimensions of length that can be formed out of c, G and e/4πε0 is [c is the velocity of light, G is the universal constant of gravitation and e is charge]

A student measured the diameter of a small steel ball using a screw gauge of least count 0.001 cm. The main scale reading is 5 mm and zero of circular scale division coincides with 25 divisions above the reference level. If screw gauge has a zero error of –0.004 cm, the correct diameter of the ball is

• 0.521 cm

• 0.525 cm

• 0.529 cm

• 0.053

The length, breadth and thickness of a block are given by l = 12 cm, b = 6 cm and t = 2.45 cm. The volume of the block according to the idea of significant figures should be

• 1 × 10² cm³

• 2 × 10² cm³

• 1.76 × 10² cm³

• None of these

In a system of units if force (F), acceleration (A), and time (T) are taken as fundamental units, then the dimensional formula of energy is:

• FA²T

• FAT²

• F²AT

• FAT

A force F is given by F =at + bt² ,where, t is time. What are the dimensions of a and b ?

• $\left[\mathrm{M} \mathrm{L} {\mathrm{T}}^{ -1}\right] \mathrm{and} \left[\mathrm{M} \mathrm{L} {\mathrm{T}}^0\right]$

• $\left[ \mathrm{M} \mathrm{L} \mathrm{T}{ }^{-3}\right] \mathrm{and} \left[\mathrm{M} {\mathrm{L}}^2 {\mathrm{T}}^4\right]$

• $\left[\mathrm{M} \mathrm{L} {\mathrm{T}}^{ -4}\right] \mathrm{and} \left[\mathrm{M} \mathrm{L} {\mathrm{T}}^1\right]$

• $\left[\mathrm{M} \mathrm{L} {\mathrm{T}}^{ -3}\right] \mathrm{and} \left[\mathrm{M} \mathrm{L} {\mathrm{T}}^{ -4}\right]$

Dimensions of resistance in an electrical circuit, in terms of dimension of mass M, of length L, of time T and of current I, would be

• [ M L² T^-3 I^-1]

• [M L² T^-1]

• [M L² T^-1 I^-1]

• [M L² T^-3 I^-2 ]

The physical quantity having the dimensions [ M^-1 L^-3 T³ A² ] is

• resistance

• resistivity

• electrical conductivity

• electromotive force