Units & measurements practice · Easy

Dimensions of frequency are

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

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 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:

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.

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:

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

The physical quantity angular momentum has the same dimensions as that of

The displacement of an oscillating particle is given by $y=A \sin (B x+C t+D)$. The dimensional formula for $(A B C D)$ is

Statement-I: Solid angle is dimensionless quantity and it is a supplementary quantity.
Statement-II: All supplementary quantities are dimensionless.

Statement-I: The MKS system is a coherent system of units
Statement-II: In SI, joule is the unit for all forms of energy

A force defined by $F=\alpha t^2+\beta t$ acts on a particle at a given time $t.$ The factor which is dimensionless, if $\alpha$ and $\beta$ are constants, is:

The dimensional formula for magnetic flux is

A force is represented by $F=a x^2+b t^{\frac{1}{2}}$
Where $x=$ distance and $t=$ time. The dimensions of $b^2 / a$ are:

A physical quantity A is related to four observables a,b,c and d as follows $\;A = \frac{{{a^2}{b^3}}}{{c\sqrt d }}$ The percentage errors of measurement in a,b,c and d are 1%, 3%, 2% and 2% respectively. What is the percentage error in the quantity A?

Which of the following statement(s) is/are incorrect?

Identify the pair whose dimensions are equal.

Temperature can be expressed as a derived quantity in terms of any of the following

Statement-I: Systematic errors can be removed completely.
Statement-II: the cause of systematic errors can be known.

The dimensional formula for Reynold's number is

10 divisions on the main scale of a Vernier calliper coincide with 11 divisions on the Vernier scale. If each division on the main scale is of 5 units, the least count of the instrument is:

The dimensions of calorie are

The unit of self inductance of a coil is

Statement-I: If error in measurement of mass is $2 \%$ and that in measurement of velocity is $5 \%$ than error in measurement of kinetic energy is $6 \%$.
Statement-II: Error in kinetic energy is $\frac{\Delta K}{K}=\left(\frac{\Delta m}{m}+2 \frac{\Delta v}{v}\right)$

Statement-I: Plane angle is dimensionless quantity.
Statement-II : All unitless quantities are dimensionless

A physical quantity is measured and its value is found to be nu where where n= numerical value and u= unit. Then which of the following relations is true

SI unit of electric intensity is