Units and Measurements PYQs

The speed of light in vacuum is taken as unity. If light takes 6 min 40 s to reach the Earth from the Sun, the distance between the Sun and the Earth in new unit is:

Each side of a metallic cube of mass 5.580 kg is measured to be 9.0 cm. Keeping the significant figures in view, the density of the material of the cube can be best expressed as X × 10³ kg m⁻³ where the value of X is:

In a vernier caliper, 20 VSD coincide with 16 MSD (each division length 1 mm). The least count of the vernier calipers is:

Consider the diameter of a spherical object being measured with the help of Vernier callipers. Suppose this 10 Vernier Scale Divisions (V.S.D.) are equal to 9 Main Scale Divisions (M.S.D.). The least division in the M.S. is 0.1 cm and the zero of V.S. is at x = 0.1 cm when the jaws of Vernier callipers are closed. If the main scale reading for the diameter is M = 5 cm and the number of coinciding vernier division is 8, the measured diameter after zero error correction, is

A physical quantity $P$ is related to four observations $a$, $b$, $c$ and $d$ as follows: $$P = a^3 b^2 c \sqrt{d}$$ The percentage errors of measurement in a, b, c and d are 1%, 3%, 2%, and 4% respectively. The percentage error in the quantity P is

In a vernier calipers, $(N+1)$ divisions of vernier scale coincide with $N$ divisions of main scale. If $1\,\text{MSD}$ represents $0.1\,\text{mm}$, the vernier constant (in cm) is:

The quantities which have the same dimensions as those of solid angle are:

A force defined by F = αt² + βt acts on a particle at a given time t. The factor which is dimensionless, if α and β are constants, is:

A metal wire has mass (0.4 ± 0.002) g, radius (0.3 ± 0.001) mm and length (5 ± 0.02) cm. The maximum possible percentage error in the measurement of density will nearly be:

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

Plane angle and solid angle have:

The area of a rectangular field (in m²) of length 55.3 m and breadth 25 m after rounding off the value for correct significant digits is:

If $E$ and $G$ respectively denote energy and gravitational constant, then $\dfrac{E}{G}$ has the dimensions of:

A screw gauge gives the following readings when used to measure the diameter of a wire. Main scale reading: 0 mm Circular scale reading: 52 divisions Given that 1 mm on main scale corresponds to 100 divisions on the circular scale. The diameter of the wire from the above data is:

If force [F], acceleration [A] and time [T] are chosen as fundamental physical quantities, find the dimensions of energy.

A screw gauge has least count of 0.01 mm and there are 50 divisions in its circular scale. The pitch of the screw gauge is :

Dimensions of stress are :

Taking into account the significant figures, what is the value of 9.99 m − 0.0099 m?

The main scale of a vernier callipers has n divisions/cm. n divisions of the vernier scale coincide with (n − 1) divisions of the main scale. The least count of the vernier callipers is,

A student measured the diameter of a small steel ball using a screw gauge of least count 0.001 cm. The main scale reading is 5 mm and zero of circular scale division coincides with 25 divisions above the reference level. If screw gauge has a zero error of -0.004 cm, the correct diameter of the ball is:

A physical quantity having dimensions of length can be formed using the quantities $c$, $G$ and $\dfrac{e^2}{4\pi\varepsilon_0}$. Which of the following combinations represents length?

Planck’s constant $(h)$, speed of light in vacuum $(c)$ and Newton’s gravitational constant $(G)$ are three fundamental constants. Which of the following combinations of these has the dimension of length?

In dimension of critical velocity vc of liquid flowing through a tube are expressed as (ηˣ ρʸ rᶻ), where η, ρ and r are the coefficients of viscosity of liquid, density of liquid and radius of the tube respectively, then the values of x, y and z are given by:

If force (F), velocity (V) and time (T) are taken as fundamental units, then the dimensions of mass are:

Equal masses of H₂, O₂ and methane have been taken in container of volume V at temperature 27°C under identical conditions. The ratio of the volumes of gases H₂ : O₂ : methane would be:

In an experiment four quantities $a$, $b$, $c$ and $d$ are measured with percentage errors $1\%$, $2\%$, $3\%$ and $4\%$ respectively. Quantity $P$ is calculated as follows: $$P = \frac{a^3 b^2}{cd}$$ % error in P is:

The dimensions of $\left(\mu_0\varepsilon_0\right)^{-1/2}$ are:

The density of material in CGS system of units is 4 g/cm³. In a system of units in which unit of length is 10 cm and unit of mass is 100 g, the value of density of material will be:

If the dimensions of a physical quantity are given by [$M^a$ $L^b$ $T^c$], then the physical quantity will be:

Which two of the following five physical parameters have the same dimensions? (a) energy density (b) refractive index (c) dielectric constant (d) Young's modulus (e) magnetic field

If the error in the measurement of radius of a sphere is 2%, then the error in the determination of volume of the sphere will be

Which of the following quantities have the same dimensional formula?

The velocity v of a particle at time t is given by v = at + (b/(t + c)), where a, b and c are constants. The dimensions of a, b and c are respectively:

The ratio of the dimensions of Planck's constant and that of the moment of inertia is the dimension of: