Units & measurements practice · Mixed difficulty

The density of a material in CGS system of units is $4g/c{m^3}$, In a system of units which unit of length is 10 cm and unit of mass is 100 g , the value of density of material will be

The two full turns of circular scale of screw gauge cover a distance of $1 \mathrm{~mm}$ on scale. The total division on circular scale is 50 further if found that screw gauge has a zero error of $-0.01 \mathrm{~mm}$. While measuring the diameter of thin wire a student notes the main scale reading of $2 \mathrm{~mm}$ and the no of circular scale division in line with the main scale as 25. The diameter of wire is

The least count of a stop watch is 0.2 s. The time of 20 oscillations of a pendulum is measured to be 25 s. The percentage error in the measurement of time will be

newton-second is the unit of

Which of the following physical quantities represent the dimensions of $b / a$ in the relation $P=\left(x^2-b\right) / a t$, where $P$ is power, $x$ is distance and '$t$' time?

To determine the Young’s modulus of a wire, the formula is $Y = \frac{F}{A} \times \frac{L}{{\Delta L}}$; where L= length, A= area of cross-section of the wire, ${\Delta L}$= change in length of the wire when stretched with a force F. The conversion factor to change it from CGS to MKS system is

Which of the following combinations have the dimensions of time? $L-C-R$ represent inductance, capacitance and resistance, respectively.

The dimensional representation of Planck's constant is identical to that of

From the equation $\tan \theta = \frac{{rg}}{{{v^2}}},$one can obtain the angle of banking $\theta$ for a cyclist taking a curve (the symbols have their usual meanings). Then say it is,

If momentum $P,$ area $A$ and time $T$ are taken to be the fundamental quantities, then the dimensional formula for energy is

A student performs an experiment for determination of $\mathrm{g}\left( { = \frac{{4{\mathrm{\pi }^2}l}}{{{T^2}}}} \right),\mathrm{\;}l \approx 1\mathrm{m},$, and he commits an error of $\Delta l.$. For T he takes the time of n oscillations with the stop watch of least count ∆T and he commits a human error of 0.1 s. For which of the following data, the measurement of g will be most accurate?

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,

Which of the following pairs does not have similar dimensions

Statement-I: Electromotive force is expressed in newton.
Statement-II: Electric intensity is expressed in $\mathrm{NC}^{-1}$

Which of the following quantities have the same dimensions?
a. Surface tension $\quad$ b. Spring constant $\quad$ c. Tension

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.