Units & measurements practice · Medium

A vernier callipers (with least count = 0.1 mm) has 20 divisions of the vernier scale. The main scale divisions are of

In Vander walls equation $(P + \frac{a}{{{V^2}}})(V - b) = RT,$ The dimensions of b are

A sextant is used to measure

Which of the following cannot be regarded as an essential characteristic of a unit of measurement?

A thin copper wire of length $l$ metre increases in length by 2% when heated through ${10^\mathrm{o}}C.$. What is the percentage increase in area when a square copper sheet of length l metre is heated through ${10^\mathrm{o}}C.$

If energy $E$, volume $V$ and time $T$ are taken as fundamental units, the dimensional formula of the force will be

The dimensional formula of tension force is

“Pascal-Second” has dimension of

The quantities $x = \frac{1}{{\sqrt {{\mu _0}{\varepsilon _0}} }},\,\,y = \frac{E}{B}$ and $z = \frac{l}{{CR}}$ are defined, where $C$ is capacitance, $R$ is resistance, $l$ is length, $E$ is electric field, $B$ is magnetic field, ${\varepsilon _0}$ is free space permittivity and ${\mu _0}$ is permeability, respectively. Then,

The errors in the measurement which arise due to unpredictable fluctuations in temperature and voltage supply are

A calorie is a unit of heat energy and its value is $4.18 \mathrm{~J}$ where $1 \mathrm{~J}=1 \mathrm{~kg}-\mathrm{m}^2 / \mathrm{s}^2$. Suppose we use a new system of units in which unit of mass equals $\alpha \,\mathrm{kg}$, the unit of length equals $\beta \,\mathrm{m}$ and the unit of the time is $\gamma \,\mathrm{sec}$. Then the value of a calorie in the new system of units is:

The dimensional formula of angular velocity is

The dimensions of induced emf in MKS is

The pressure on a square plate is measured by measuring
the force on the plate and length of the sides of the plate by using the formula $P = \frac{F}{{{l^2}}}$. If the maximum errors in the measurement of force and length are 4% and 2% respectively, then the maximum error in the measurement of pressure is

The quantity $X = \frac{{{\varepsilon _0}LV}}{t}:{\varepsilon _0}$ is the permittivity of free space, L is length, V is potential difference and t is time. The dimensions of X are same as that of

An approximate value of number of seconds in an year is $\pi \times 10^7$. Determine the $\%$ error in this value.

Assertion: The unit vectors $\hat{i}, \hat{j}$ and $\hat{k}$ have units of distance and dimensions $\left[M^0 {L}^1 {T}^0\right]$
Reason: The product of a scalar and a vector is a new scalar.

The dimensional formula for gravitational constant is

One femtometre is equivalent to

Ins is defined as

The unit of the coefficient of viscosity in S.I. system is

Which of the following groups has different dimensions?

The value of universal gas constant is $R = 8.3$ J/K-mol. The value of R in atmosphere litre per Kelvin mol

Instrumental error can be caused due to

If error in measuring diameter of a circle is $4 \%$, the error in measuring radius of the circle would be

A cube of metal is subjected to a hydrostatic pressure of 4 GPa. The percentage change in the length of the side of the cube is close to (Take bulk modulus of metal, $B\, = \,8\, \times \,\mathrm{1}{\mathrm{0}^{\mathrm{10}}}\,\,\,\mathrm{Pa)}$

Density of wood is 0.5 gm/cc in the CGS system of units. The corresponding value in MKS units is

The percentage error in measuring, $M, L$ and $T$ are $1 \%, 3 \%$ and $\frac{3}{2} \%$ respectively. Then the percentage error in measuring the physical quantity with dimensions ${ML}^{-1} {~T}^{-1}$ is

Which of the following has the least number of significant figures?

Assertion: In $y=A \sin (\omega t-k x),(\omega t-k x)$ is dimensionless.

Reason: Because dimension of $\omega=\left[M^0 L^0 T\right]$.