Units & measurements practice · Medium

A public park, in the form of a square, has an area of $\left( {100 \pm 0.2} \right){\mathrm{m}^2}$ . The side of park is

The velocity of water waves (v) may depend on their
wavelength l, the density of water r and the acceleration
due to gravity, g. The method of dimensions gives the
relation between these quantities is

The units of length, velocity and force are doubled. Which of the following is the correct change in the other units?

Out of the following which pair of quantities do not have same dimensions

Assertion: The measure of a physical quantity is independent of the system of units.

Reason: The smaller is unit, bigger is the measure of the physical quantity and vice-versa.

Linear momentum and angular momentum have the same dimensions in

The thrust developed by a rocket-motor is given by $F = mv + A\left( {{p_1} - {p_2}} \right)$, where m is the mass of the gas ejected per unit time, $v$ is velocity of the gas, A is area of cross-section of the nozzle, ${p_1}.{p_2}$ are the pressures of the exhaust gas and surrounding atmosphere. The formula is dimensionally

A bee of mass $0.000087 \mathrm{~kg}$ sits on a flower of mass $0.0123 \mathrm{~kg}$. What is the total mass supported by the stem of the flower up to appropriate significant figures?

Coefficient of thermal conductivity has the dimensions

Assertion : Units of Rydberg constant $R$ are $m$

Reason : It follows from Bohr's formula $\bar{v}=R\left(\frac{1}{n_1^2}-\frac{1}{n_2^2}\right)$, where the symbols have their usual meaning.

Statement I: The value of velocity of light is $3 \times 10^8 \mathrm{~ms}^{-1}$ and acceleration due to gravity is $10 \mathrm{~ms}^{-2}$ and the mass of proton is $1.67 \times 10^{-27} \mathrm{~kg}$.
Statement II: The value of time in such a system is $3 \times 10^7 \mathrm{~s}$.

The dimensional formula of magnetic dipole moment is

Dimension of force is

The difference between the true value and measured value is called

The density of a material in CGS system of units is $4g/c{m^3}$, In a system of units which unit of length is 10 cm and unit of mass is 100 g , the value of density of material will be

Assertion: The equation $y=x+t$ cannot be true, where $x, y$ are distance and $t$ is time.

Reason: Quantities with different dimensions cannot be added

A sextant is a double reflecting navigation instrument. Which of the following physical quantity, it can measure?

Unit of Stefan's constant is

The dimensional formula for impulse is

Assertion: Two students measure the length of a stick as $1.3 \mathrm{~m}$ and $1.30 \mathrm{~m}$. Both the measurements are equally accurate.

Reason: The zero at the end of a number is always meaningless.

The equation of state of a real gas is given by $\left(P+\frac{a}{V^2}\right)(V-b)=R T,$ where $P, V$ and $T$ are pressure, volume and temperature respectively and $R$ is the universal gas constant. The dimensions of $\frac{a}{b^2}$ is similar to that of:

Universal time is based on

The dimensional formula for entropy is

The radius of gold nucleus is 41.3 fermi. Express its volume in $\mathrm{m}^3$.

The dimensional formula of relative density is

Which two of the following five physical parameters have the same dimensions?
(A) Energy density

(B) Refractive index
(C) Dielectric constant
(D) Young's modulus
(E) Magnetic field

If Q denote the charge on the plate of a capacitor of
capacitance C then the dimensional formula for
$\frac{{{Q^2}}}{C}$ is

Which of the following is/are the units of strength of magnetic field at a point?

Faraday is the unit of

The difference in the lengths of a mean solar day and a side real day is about