Units & measurements practice · Medium

What is dimensional formula of thermal conductivity?

$erg - {m^{ - 1}}$ can be the unit of measure for

A rectangular beam which is supported at its two ends and leaded in the middle with weight w sags by an amount δ such that $\delta = \frac{{w{l^3}}}{{4Y{d^3}}},\;$, where $l,d$ and Y represent length, depth and elasticity respectively. Guess the unknown factor using dimensional considerations

Given that $r = {m^2}$ sin pt, where t represents time. If the unit of m is N, then the unit of r is

Parsec is a unit of

Which is different from others by units

The dimensional formula of angular velocity is

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

The radius of the sphere is $\left( {4.3 \pm 0.1} \right)$ cm. The percentage error in its volume is

If the velocity of light $\left( C \right)$ gravitational constant $\left( G \right)$ and Planck’s constant $h$ are chosen as fundamental units,then the dimensions of mass in new system is

A cube has numerically equal volume and surface area. The volume of such a cube is

Which of the following is not the unit of time?

The difference between the true value and measured value is called

The dimension of stopping potential ${V_0}$ in photoelectric effect in units of Planck’s constant $h,$ speed of light $c$ and gravitational constant $G$ and ampere $A$ is

An atomic clock makes use of

The dimension of torque is

The dimensions of electric dipole moment are

Assertion : Avogadro’s number is the number of atoms
in one gram mole.
Reason : Avogadro’s number is a dimensionless constant.

Which physical quantities have the same dimension

In an experiment, to measure the height of a bridge by dropping stone into water underneath, if the error in measurement of time is 0.1s at the end of 2s, then the error in estimation of height of bridge will be

In a measurement, it is asked to find modulus of elasticity per unit torque applied on the system. The measured quantity has dimension of $\left[M^a L^b T^c\right].$ If $b=3$, the value of $c$ is

If E,M,L and G denote energy, mass, angular momentum and gravitational constant respectively, then the quantity $\left( {E{L^2}/{M^5}{G^2}} \right)$ has the dimensions of

Assertion : Number of significant figures in 0.005 is one and that in 0.500 is three
Reason : This is because zeros are not significant.

The energy (E), angular momentum (L) and universal gravitational constant (G) are chosen as fundamental quantities. The dimensions of universal gravitational constant in the dimensional formula of Planck’s constant (h) is

The work done by a battery is $W = \varepsilon \Delta q$ , where $\Delta q$ charge transferred by battery, $\varepsilon$ = emf of the battery. What are dimensions of emf of battery?

The SI unit of electrochemical equivalent is

Let L denote the self-inductance of coil which is in series with a capacitor of capacitance C. Which of the following has the unit second?

The SI unit of gravitational potential is

If a book with many printing errors contains four different formulae for the displacement $y$ of a particle undergoing a certain periodic motion.
(1) $y=a \sin \frac{2 \pi t}{T}$
(2) $y=a \sin v T$
(3) $y=\frac{a}{T} \sin \frac{t}{a}$
(4) $y=(a \sqrt{2})\left(\sin \frac{2 \pi t}{T}+\cos \frac{2 \pi t}{T}\right)$
where $a$ is the maximum displacement of the particle, $v$ is the speed of particle, $T$ is the time period of motion. Then dimensionally

SI unit of permittivity is