Units & measurements practice · Mixed difficulty

If electronic charge $e,$ electron mass $\mathrm{m}$, speed of light in vacuum $\mathrm{c}$ and Planck's constant $\mathrm{h}$ are taken as fundamental quantities, the permeability of vacuum $\mu_0$ can be expressed in units of

Given $R_1=(3.0 \pm 0.1) \Omega, R_2=(6.0 \pm 0.2) \Omega$, then calculated as $\frac{1}{R_P}=\frac{1}{R_1}+\frac{1}{R_2}$ is given by

The damping force of an oscillating particle is observed to be proportional to velocity. The constant of proportionality can be measured in

Statement-I: Electric current is a scalar
Statement-II: All fundamental physical quantities are scalars

Which one of the following groups have quantities that do not have the same dimensions?

Which the following is/are correct?
I. Pressure = energy per unit area
II. Pressure = energy per unit volume
III. Pressure = force per unit volume
IV. Pressure = momentum per unit volume per unit time

Assertion : A.U. is much bigger than $\mathop {\text{A}}\limits^{\text{o}} .$
Reason: A.U. stands for astronomical unit and A stands for Angstrom.

The dimensions of specific resistance in terms of charge $Q$ is

The equation of stationary wave is: $y=2 a \sin \left(\frac{2 \pi n t}{\lambda}\right) \cos \left(\frac{2 \pi x}{\lambda}\right)$. Which of the following is NOT correct

When two quantities are divided, the relative error in the
result is given by

A physical quantity $Q$ is found to depend on observables $x, y$, and $z$, obeying relation $Q=x^3 y^2 / z$. The percentage error in the measurements of $x, y$, and $z$ are $1 \%, 2 \%$ and $4 \%$ respectively. What is percentage error in the quantity $Q$?

The dimensions of $(a \cdot b)$ in the equation $P=\frac{a-t^2}{b x}$ where $P$ is power, $x$ is distance and $t$ is time, are

The unit of absolute permittivity is

The heat generated in a circuit depends on resistance (R), current (I) and time of flow (t). If maximum errors in the above are 1%, 0.5%, 1% respectively error in measurement of power is ($P = {i^2}R$)

The unit of viscosity in the CGS system is poise (P) and that in $\mathrm{SI}$ is poiseuille (Pl). Which of the following statement is correct?

In the determination of Young’s modulus $\left( {Y = \frac{{4\;MLg}}{{\pi \;\ell {d^2}}}} \right)$ by using Searle’s method, a wire of length L=2m and diameter d=0.5mm is used. For a load M=2.5 kg, an extension $\ell = 0.25mm$ in the length of the wire is observed. Quantities d and $\ell$ are measured using a screw gauge and a micrometer, respectively. They have the same pitch of 0.5 mm. The number of divisions on their circular scale is 100. The contributions to the maximum probable scale is 100. The contributions to the maximum probable error of the Y measurement

Light Year is a unit of

What is the SI unit of electron mobility?

Of the following quantities, which one has dimensions
different from the remaining three?

$\frac{{E}^2}{\mu_0}$ has the dimensions (${E}=$ electric field, $\mu_0=$ permeability of free space)

The number of significant figures in the numbers $4.8000 \times {10^4}$ and 48000.50 are respectively

Which of the following sets of quantities have same dimensional formula?

Dimensions of kinetic energy are

The unit of expression ${\mathrm{\mu }_0}{\mathrm{\varepsilon }_0}$ are

Assertion : Force cannot be added to pressure.

Reason : Because their dimensions are different.

The unit of permittivity of free space ${\varepsilon _0}$ is

Statement I: The distance covered by a body is given by $s=u+\frac{1}{2} \frac{a}{t}$, where the symbols have usual meaning.

Statement II: We can add, substract or equate quantities which have same dimensions.

Which pair do not have equal dimensions?

The wrong unit conversion among the following is

Unit of electric flux is