Units & measurements practice · Mixed difficulty

The dimensions of $\left(\mu_0 \varepsilon_0\right)^{-1 / 2}$ are

The maximum static friction on a body is $F = \mathrm{\mu }N$. Here, N= normal reaction force on the body $\mathrm{\mu } =$ coefficient of static friction. The dimensions of μ are

The physical quantities not having same dimensions are

Statement-I: The size (u) of the unit of physical quantity and its numerical magnitude (n) are related to each other by the relation $\mathrm{nu}=$ constant
Statement-II: Numerical value is inversely proportional to the size of the unit chosen.

Assertion : When we change the unit of measurement of a
quantity, its numerical value changes.
Reason : Smaller the unit of measurement smaller is its
numerical value.

A suitable unit for gravitational constant is

A screw gauge has least count of $\mathrm{0}\mathrm{.01 mm}$ and there are $\mathrm{50}$ divisions in its circular scale. The pitch of the screw gauge is :

Wavelength of ray of light is 0.00006 m. It is equal to

Statement-I: Two quantities which are to be added must have the same dimensions
Statement-II: Two quantities which are to be multiplied may have the same dimensions.

Given a charge $q,$ current $I$ and permeability of vacuum $\mu_0.$ Which of the following quantity has the dimension of momentum?

Assertion : Rate of flow of a liquid represents velocity of flow.

Reason : The dimensions of rate of flow are $[M L T]$.

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A) : In Vernier calliper if positive zero error exists, then while taking measurements, the reading taken will be more than the actual reading.

Reason (R) : The zero error in Vernier Calliper might have happened due to manufacturing defect or due to rough handling.
In the light of the above statements, choose the
correct answer from the options given below:

A thin $1 \mathrm{~m}$ long rod has a radius of $5 \mathrm{~mm}$. A force of $50 \pi \, \mathrm{kN}$ is applied at one end to determine its Young's modulus. Assume that the force is exactly known. If the least count in the measurement of all lengths is $0.01 \mathrm{~mm}$, which of the following statements is false?

Which of the following is the smallest unit

$1kWh\; =$

Velocity of sound in a gas is given by $v=\sqrt{\frac{\gamma p}{\rho}}$. Dimensional formula for $\gamma$ is

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 value of Planck's constant in SI unit is

Statement-1: Two or more than two physical quantities may have same dimension.

Statement-2: A physical quantity may have several units.

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

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

The dimensional formula for $\frac{(\text {Capacitance})(\text {Electrostatic Potential})^2}{(\text {Permitivity})(\text {Electric field})^2}$ is same as that of:

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

Error in measurement of radius of sphere is 4% then maximum % error in volume is

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