Units & measurements practice · Medium

If 1 g cm ${\mathrm{s}^{ - 1}} = x$ newton-second, then the number x is equal to

The dimensional formula for impulse is same as the dimensional formula for

Which of the following is the most accurate instrument for measuring length?

In an experiment the angles are required to be measured using an instrument. 29 divisions of the main scale exactly coincide with the 30 divisions of the vernier scale. If the smallest division of the main scale is half-a-degree $\left( { = 0.5^\circ } \right),$ then the least count of the instrument is

If $v = \frac{A}{t} + B{t^2} + C{t^3}$ , where $v$ is velocity, t is time and A,B and C are constants, then the dimensional formula of B is

One shake is equal to

Dimensions of coefficient of viscosity are

A spherometer has 100 equal divisions marked along the periphery of its disc and one full rotation of the disc advances on the main scale by $0.01 \mathrm{~cm}$. The least count of this system is

From the dimensional consideration, which of the following equation is correct

To measure the distance of a planet from the Earth, ______ method is used.

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

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 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