Units & measurements practice · Mixed difficulty

Taking frequency $f$, velocity $v$ and density $\rho$ to be the fundamental quantities, then the dimensional formula for momentum will be

Given that $:y = A\sin \left[ {\left( {\frac{{2\pi }}{\lambda }} \right)\;\left( {ct - x} \right)} \right]$ where, y and x are measured in metre. Which of the following statements is true?

The concorde is the fastest airlines used for commercial service. It can cruise at 1450 mile per hour (about two times the speed of sound or in other words mach 2). What is it in m/s?

$S = A(1 - {e^{ - Bxt}})$ where S is speed and x is displacement. Then unit of B is

If C,R,L and I denote capacity, resistance, inductance and electric current respectively, the quantities having the same dimensions of time are $\left( 1 \right)\,CR,\,\,\left( 2 \right)\,\frac{L}{R}\,,\,\,\left( 3 \right)\,\sqrt {LC} \,\,\left( 4 \right)\,L{I^2}$

In a new system of units, unit f mass is 10 kg, unit of length is 1 km and unit of time is 1 min. The value of 1 joule in this new hypothertical system is

The dimensional formula for impulse is

Unit of magnetic moment is

Statement-I: Surface tension and spring constant have the same dimensions.
Statement-II: Both are equivalent to force per unit length

You may not know integration. But using dimensional analysis you can check or prove results. In the integral $\int \frac{d x}{\left(2 {ax}-x^2\right)^{1 / 2}}=a^n \sin ^{-1}\left(\frac{x}{a}-1\right)$ the value of $n$ should be-

The equation which is dimensionally correct among the following is

Dimension of R is

A quantity X is given by ${\varepsilon _0}L\frac{{\Delta V}}{{\Delta t}},\;$, where ${\varepsilon _0}$ is the permittivity of free space, L is a length, ${\Delta V}$ is a potential difference and ${\Delta t}$ is a time interval. The dimensional formula for X is the same as that of

The unit of physical quantity obtained by the line intergral of electric field is

The respective number of significant figures for the numbers 23.023, 0.0003 and $2.1 \times {10^{ - 3}}$ are

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,

In $\mathrm{\;S} = a + bt + c{t^2}$. S is measured in metre and t in second. The unit of c is

In an experiment, the following observation’s were recorded: $L = 2.820\;m$, M=3.00 kg,l=0.087 cm, diameter D=0.041 cm. Taking g=9.81 $m/{s^2}$ using the formula,
$Y = \frac{{4MgL}}{{\pi {D^2}l}}$, the maximum permissible error in Y is

The external and internal diameters of a hallow cylinder are measured to be $(4.23 \pm 0.01)\,cm$ and $(3.89 \pm 0.01)\,cm$. The thickness of the wall of the cylinder is

The Vander Waal’s equation of state for real gases is given as $\left( {P + \frac{a}{{{V^2}}}} \right)\left( {V - b} \right) = nRT$ which of the following terms has dimensions different from that of energy

Assertion A: If in five complete rotations of the circular scale, the distance travelled on main scale of the screw gauge in 5 mm and there are 50 total divisions on circular scale, then least count of screw gauge is 0.002 cm.
Reason R: Least count $=\frac{\text { Pitch }}{\text { Total divisions on circular scale }}$

A student performs an experiment for determination of $g = \frac{{4{\pi ^2}l}}{{{T^2}}}$ and he commits an error of ∆l. For that he takes the time of n oscillations with the stop watch of least count $\Delta$T and he commits a human error of 0.1 sec. For which of the following data, the measurement of g will be most accurate $\Delta l\,\,\Delta T\,\,n\,\,Ampli.of\,oscill$

1 Parsec is equal to

$\left[ {\mathrm{M}{\mathrm{L}^2}{\mathrm{T}^{ - 2}}} \right]$ are dimensions of