Units and Measurement

If σ = surface change density, ε = electric permittivity, the dimensions of $\frac{\mathrm{\sigma }}{\mathrm{\epsilon }}$ is same as

• electric force

• electric field intensity

• pressure

• electric charge

A gas bubble forms an explosion under water which oscillate with a period T ∝ p^aρ^bE^c, where p is the static pressure, ρ is the density ofwater and E is the total energy of explosion. Then, the values of a, b and c will be

• $- \frac{5}{6}, \frac{1}{2}, \frac{1}{3}$

• $\frac{2}{5}, \frac{1}{3}, \frac{1}{4}$

• $\frac{4}{5}, \frac{9}{8}, \frac{1}{2}$

• $\frac{3}{2}, \frac{1}{4}, \frac{5}{6}$

The physical quantity having dimensions [M^-1L^-3T³A²] is

• resistance

• resistivity

• electrical conductivity

• electromotive force

The dimensions of σb⁴ are (where, σ = Stefan's constant and b = Wein's constant).

• [ M⁰L⁰T⁰ ]

• [ ML⁴T^-3 ]

• [ ML^-2T ]

• [ ML⁶T^-3 ]

The SI unit of gravitational potential is

• J

• J-kg^-1

• J-kg

• J-kg²

The potential energy of a particle varies with distance x from a fixed origin as $\mathrm{V} = \left(\frac{\mathrm{A}\sqrt{\mathrm{x}}}{\mathrm{x} + \mathrm{B}}\right)$ ; where A and B are constants. The dimensions of AB are

• $\left[{\mathrm{ML}}^{5/2}{\mathrm{T}}^{-2}\right]$

• $\left[{\mathrm{ML}}^2{\mathrm{T}}^{-2}\right]$

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

• $\left[{\mathrm{ML}}^{7/2}{\mathrm{T}}^{-2}\right]$

The dimensions of kinetic energy is

• [M²L²T]

• [ML²T]

• [ML²T^-2]

• [ML²T^-1]

If the figure below represents a parabola, identify the physical quantities  representing Y and X for constant acceleration

• X = time, Y = velocity

• X = velocity, Y = time

• X = time, Y= displacement

• X = time, Y = acceleration

The dimensional formula of magnetic flux is

• [MLT^-2A^-1]

• [ML²T^-1A^-1]

• [ML²T^-1A^-2]

• [ML²T^-2A^-1]

A physical quantity A is related to four observables a, b, c and d as follows :

$\mathrm{A} = \frac{{\mathrm{a}}^2{\mathrm{b}}^3}{\mathrm{c}\sqrt{\mathrm{d}}}$ . The percentage errors of measurement in a, b, c and d are 1%, 3%, 2% and 2% respectively. What is the percentage error in the quantity A ?

• 12 %

• 7 %

• 5 %

• 14 %