Units & Measurement

One main scale division of a Vernier calliper is equal to 1 mm and the number of divisions on the Vernier scale is 10 . When both the jaws touch each other, the Vernier scale shifts to the left of zero of the main scale in such a way that $...

Consider that $\sigma_s, k_B, b$ represents Stefan-Boltzmann constant, Boltzmann constant and Wien's displacement law constant, respectively. The dimension of $\sigma_s k_B^{-1} b$ is

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

Each side of a metallic cube of mass 5.580 kg is measured to the 9.0 cm . Keeping the significant figures in view, the density of the material of the cube can be best expressed as $X \times 10^3 \mathrm{~kg} \mathrm{~m}^{-3}$ where the valu...

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:

A balloon is made of a material of surface tension $S$ and its inflation outlet (from where gas is filled in it) has small area $A$. It is filled with a gas of density $\rho$ and takes a spherical shape of radius $R$. When the gas is allowe...

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...

Consider the diameter of a spherical object being measured with the help of a Vernier callipers. Suppose its 10 Vernier Scale Divisions (V.S.D.) are equal to its 9 Main Scale Divisions (M.S.D.). The least division in the M.S. is 0.1 cm and ...

The potential energy of a particle moving along \(x\)-direction varies as \(V=\frac{A x^2}{\sqrt{x}+B}\). The dimensions of \(\frac{A^2}{B}\) are:

The pitch of an error free screw gauge is \(1 \mathrm{~mm}\) and there are 100 divisions on the circular scale. While measuring the diameter of a thick wire, the pitch scale reads \(1 \mathrm{~mm}\) and \(63^{\text {rd }}\) division on the ...

In an electrical circuit, the voltage is measured as \(V=(200 \pm 4)\) volt and the current is measured as \(I=(20 \pm 0.2)\) A. The value of the resistance is:

A force defined by \(F=\alpha t^2+\beta t\) acts on a particle at a given time \(t\). The factor which is dimensionless, if \(\alpha\) and \(\beta\) are constants, is:

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

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

The mechanical quantity, which has dimensions of reciprocal of mass \((\mathrm{M}^{-1})\) is :

The diameter of a spherical bob, when measured with vernier callipers yielded the following values : \(3.33 \mathrm{~cm}, 3.32 \mathrm{~cm}, 3.34 \mathrm{~cm}, 3.33 \mathrm{~cm}\) and \(3.32 \mathrm{~cm}\). The mean diameter to appropriate ...

A metal wire has mass \((0.4 \pm 0.002) ~\mathrm{g}\), radius \((0.3 \pm 0.001) ~\mathrm{mm}\) and length \((5 \pm 0.02) ~\mathrm{cm}\). 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 :

The percentage error in the measurement of g is : (Given that \(g = {{4{\pi ^2}L} \over {{T^2}}}\), \(L = (10\, \pm \,0.1)\) cm, \(T = (100\, \pm \,1)\) s)

The physical quantity that has the same dimensional formula as pressure is

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

Plane angle and solid angle have

The dimensions [MLT\(-\)2A\(-\)2] belong to the

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

A screw gauge gives the following readings when used to measure the diameter of a wire Main scale reading : 0 mmCircular scale reading : 52 divisionsGiven that 1 mm on main scale corresponds to 100 divisions on the circular scale. The diame...

The E and G respectively denote energy and gravitational constant, then \({E \over G}\) has the dimensions of :

Dimensions of stress are :

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 :

Taking into account of the significant figures, what is the value of \(9.99 m - 0.0099m\)?

The energy required to break one bond in DNA is 10-20 J. This value in eV is nearly :

In an experiment, the percentage of error occurred in the measurement of physical quantities A, B, C and D are 1%, 2 %, 3 %and 4 % respectively. Then the maximum percentage of error in the measurement X, where
X = $${{{A^2}{B^{1/2}}} \over...

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 physical quantity of the dimensions of length that can be formed out of c, G and \({{{e^2}} \over {4\pi {\varepsilon _0}}}\) is [c is velocity of light, G is the universal constant of gravitation and e is charge]

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

If energy (E), velocity (V) and time (T) are chosen as the fundamental quantities, the dimensional formula of surface tension will be

If dimensions of critical velocity \(\upsilon\)c of a liquid flowing through a tube are expressed as \(\left[ {{\eta ^x}{\rho ^y}{r^z}} \right]\) where \(\eta ,\rho\) and r are the coefficient of viscosity of liquid, density of liquid and...

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

The pair of quantities having same dimensions is

If an experiment four quantities a, b, c and d are measured with percentage error 1%, 2%, 3% and 4% respectively.
Quantity P is calculated as follows P \(= {{{a^3}{b^2}} \over {cd}}\) % error in P is

The damping force on an oscillator is directly proportional to the velocity. The units of the constant of proportionality are

The dimensions of \({\left( {{\mu _0}{\varepsilon _0}} \right)^{ - 1/2}}\) are

The dimensions of \({\left( {{\mu _0}{\varepsilon _0}} \right)^{ - 1/2}}\) are

The density of a material in CGS system of units is 4 g cm\(-\)3. 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

The dimension of \({1 \over 2}{\varepsilon _0}{E^2}\), where \({\varepsilon _0}\) is permittivity of free space and E is electric field, is

A student measures the distance traversed in free fall of a body, initially at rest, in a given time. He uses this data to estimate g, the acceleration due to gravity. If the maximum percentage errors in measurement of the distance and the ...

If the dimensions of a physical quantity are given by MaLbTc, then the physical quantity will be

Which two of the following five physical parameters have the same dimensions ?
1.  Energy density
2.  Refractive index
3.  Dielectric constant
4.  Young's modulus
5.  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

Dimensions of resistance in an electrical circuit, in terms of dimension of mass M, of length L, of time T and of current I, would be

The velocity v of a particle at time t is given by v = at + \({b \over {t + c}}\), where a, b and c are constants. The dimensions of a, b and c are