Units & measurements practice · Medium

Assertion: All derived quantities may be represented dimensionally in terms of the base quantities.
Reason : The dimensions of a base quantity in other base quantities are always zero.

Illuminance of a surface is measured in

In the following list, the only pair which have different dimensions, is

Dimensions of planck’s constant is:

Consider the quantities, pressure, power, energy, impulse, gravitational potential, electrical charge, temperature, area. Out of these, the only vector quantities are

Which of the following units denotes the dimensions $\left[ {\mathrm{M}{\mathrm{L}^2}/{\mathrm{Q}^2}} \right],$, where Q denotes the electric charge?

If the percentage error in measuring length and diameter of a wire is $0.1 \%$ each, then the percentage error of the resistance of the wire is

Which of the following quantity is NOT dimensionless?

The radius of a uniform wire is $r=0.021 \mathrm{~cm}$. The value of $\pi$ is given to be 3.142. What is the area of cross-section of the wire up to appropriate significant figures?

Which of the following is dimensionally correct

If the value of the resistance is 10.845Ω and the value of the current is 3.23 A, then the potential difference is 35.02935 V. its value in correct significant figures would be

Given below are two statements.

Statement (I): Dimensional formula of planck's constant is $\left[M L^2 T^{-1}\right]$

Statement (II): Dimensional formula of bulk modulus is $\left[M L^{-1} T^{-2}\right]$

The dimensions of surface tension are

Estimate the mean absolute error from the following data: $20.17,21.23,20.79,22.07,21.78$:

Which of the following pair have same dimensional formula?

Which of the following do not have the same dimensional formula as the velocity?
Given that $\mathrm{m}_0=$ permeability of free space, $\mathrm{e}_0=$ permittivity of free space, $\mathrm{n}$ = frequency, $l$ = wavelength, $\mathrm{P}=$ pressure, $\mathrm{r}$ $=$ density, $\mathrm{w}=$ angular frequency, $\mathrm{k}=$ wave number

In the equation $\left[X+\frac{a}{Y^{2}}\right][Y-b]=R T, \, X$ is pressure, $Y$ is volume, $R$ is universal gas constant $T$ is temperature. The physical quantity equivalent to the ratio $\frac{a}{b}$ is:

In the relation $x = \cos \left( {\omega t + kx} \right)$, the dimension(s) of $\omega$ is/are

Dimensions of specific heat are

Write the dimensions of $a b$ in the relation $\mathrm{P}=\frac{\mathrm{a}-\mathrm{t}^2}{\mathrm{bx}}$, where $\mathrm{P}$ is the pressure, $\mathrm{x}$ is the distance and $t$ is the time.

If C is the restoring couple per unit radian twist and I is the moment of inertia, then the dimensional representation of $2\mathrm{\pi }\sqrt {\frac{I}{C}}$ will be

Assertion : Parallex method cannot be used for measuring distances of stars more than 100 light years away.

Reason : Because parallex angle reduces so much that it cannot be measured accurately.

Assertion: Formula for kinetic energy is $\mathrm{K}=\frac{1}{2} \mathrm{mu}^2=\mathrm{ma}$

Reason : Both the equation $\mathrm{K}=\frac{1}{2} \mathrm{mv}^2$ and $\mathrm{k}=\mathrm{ma}$ are dimensionally incorrect.

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

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