Units & measurements practice · Mixed difficulty

Statement-I: Plane angle is a dimensionless quantity.
Statement-II: All supplementary quantíties are dimensionless.

The force F on the sphere of radius ‘a’ moving in a medium with velocity '$v$' is given by $F = 6\pi \eta a\upsilon$. The dimensions of η are

The dimensional formula of farad is

Which one of the following pairs of quantities and their unit is properly matched?

In a new system of units, the net force applied on a block of mass $10 \mathrm{~kg}$ moving with acceleration $10 \mathrm{~m} / \mathrm{s}^2$ is given as 100 unit of force. When the same block is moving at a speed of $20 \mathrm{~m} / \mathrm{s}$, its kinetic energy become 20 unit of energy. A liquid has a surface tension of 10 SI units. What is the magnitude of its surface tension in new system? (Dimensional formula of surface tension is $M L^0 T^{-2}$.)

Statement-I : If $u_1$ and $u_2$ are units and $n_1, n_2$ are their numerical values in two different systems then $n_1 > n_2 \Rightarrow u_1 < u_2$.
Statement-II: The numerical value of physical quantity is inversely proportional to unit.

Wave number has the dimensions of

Two quantities A and B have different dimensions. Which mathematical operation given below is physically meaningful

Which of the following unit is not of length?

The physical quantity that has no dimensions is

Assertion: Linear mass density has the dimensions of $\left[\mathrm{M}^1 \mathrm{L}^{-1} \mathrm{T}^0\right]$.
Reason: This is so because density is mass per unit volume.

Assertion : Force cannot be added to pressure.
Reason : The dimensions of force and pressure are
different.

Which two of the following quantities are
dimensionally equivalent?
(i) Force (ii) Pressure (iii) Young’s Modulus (iv) Energy

The number of significant figures in 0.06900 is

If $\left(P-\frac{a}{V^2}\right)(V-b)=n R T$, where $P, V, R$ and $T$ are pressure, volume, universal gas constant and temperature, then $\frac{a}{b^2}$ has same dimensional formula as that of

The surface tension is $T = \frac{F}{l},$ then the dimensions of surface tension are

If $\mathrm{L}$ is the inductance, $\mathrm{C}$ capacitance and $\mathrm{R}$ resistance the ratios $\mathrm{L} / \mathrm{R}$ and $\mathrm{R}-\mathrm{C}$ have the same dimensions as those of

The dimensions of stress are equal to

The unit of poynting vector is

A student when discussing the properties of a medium (except vacuum) writes

Velocity of light in vacuum = Velocity of light in medium. This formula is

A physical quantity P is described by the relation $P = {a^{1/2}}{b^2}{c^3}{d^{ - 4}}$. If the relative errors in the measurement of a, b, c and d respectively are 2%, 1%, 3% and 5% then the relative error in P will be

A physical quantity depends upon five factors, all of which have dimensions; then method of dimensional analysis

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

Dimensions of frequency are

Velocity $\left( v \right)$ and acceleration $\left( a \right)$ in two systems of units 1 and 2 are related as ${v_2} = \frac{n}{{{m^2}}}{v_1}$ and ${a_2} = \frac{{{a_1}}}{{mn}}$ respectively. Here $m$ and $n$ are constants. The relations for distance and time in two systems respectively are:

Which of the technique is not used for measuring small time intervals?

Accidental error can be minimised by

The mass of the liquid flowing per second per unit area of cross-section of the tube is proportional to (pressure difference across the ends) $^n$ and (average velocity $^m$ of the liquid. Which one of the following relation is correct?

The dimensions of ${e^2}/4\mathrm{\pi }{\mathrm{\varepsilon }_0}hc,$, where $e,\;{\mathrm{\varepsilon }_0},\mathrm{\;}h\;\mathrm{and\;}c$ are electronic charge, electric permittivity, Planck’s constant and velocity of light in vacuum respectively, are

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