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JEE physics Assertion & Reason

Units, Dimensions and Measurement · CBSE STD 12 Science (CBSE - English Medium). 25 questions.

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Assertion & Reason

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25 questions · timed · auto-graded

Question 11 Mark
Assertion : The quantity $\left(1 / \sqrt{\mu_0 \varepsilon_0}\right)$ is dimensionally equal to velocity and nemerically equal to velocity of light.
Reason : $\mu_0$ is permeability of free space and $\varepsilon_0$ is the permittivity of free space.
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Question 21 Mark
Assertion $\quad: L / R$ and $C R$ both have same dimensions.
Reason $\quad: \quad L / R$ and $C R$ both have dimension of time.
Answer
(a) Unit of quantity (L/R) is Henry/ohm.As Henry $=\mathrm{ohm} \times \mathrm{sec}$, hence unit of $L / R$ is sec i.e. ([\mathrm{L} / \mathrm{R}]=[\mathrm{T}]$.Similarly, unit of product CR is farad $\times$ ohm or, $\frac{\text { Coulomb }}{\text { Volt }} \times \frac{\text { Volt }}{\text { Amp }}$ or, $\frac{\text { Sec } \times A m p}{A m p}$ or, sec i.e. $[\mathrm{CR}]=$ $[\mathrm{T}]$ therefore $[\mathrm{L} / \mathrm{R}]$ and $[\mathrm{CR}]$ both have the same dimension.
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Question 31 Mark
Assertion : Avogadro number is the number of atoms in one gram mole.
Reason  : Avogadro number is a dimensionless constant.
Answer
(c) Avogadro number $(M)$ represents the number of atoms in 1 gram mole of an element, i.e. it has the dimensions of mole.
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Question 41 Mark
Assertion : The graph between $P$ and $Q$ is straight line, when $P / Q$ is constant.
Reason : The straight line graph means that $P$ proportional to $Q$ or $P$ is equal to constant multiplied by $Q$.
Answer
(a) According to statement of reason, as the graph is a straight line, $P \propto Q$, or $P=$ constant $\times Q$i.e. $\frac{P}{Q}=$ constant
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Question 51 Mark
Assertion : In the relation $f=\frac{1}{2 l} \sqrt{\frac{T}{m}}$, where symbols have standard meaning, $m$ represent linear mass density.
Reason : The frequency has the dimensions of inverse of time.
Answer
(b) From, $f=\frac{1}{2 l} \sqrt{\frac{T}{m}}, f^2=\frac{T}{4 l^2 m}$or, $\quad m=\frac{T}{4 l^2 f^2}=\frac{\left[M L T^{-2}\right]}{L^2 T^{-2}}=\frac{M}{L}=\frac{\text { Mass }}{\text { length }}=$ linear mass density.
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Question 61 Mark
Assertion : The time period of a pendulum is given by the formula, $T=2 \pi \sqrt{g / l}$.
Reason : According to the principle of homogeneity of dimensions, only that formula is correct in which the dimensions of L.H.S. is equal to dimensions of R.H.S.
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Question 71 Mark
Assertion : Dimensional constants are the quantities whose value are constant.
Reason : Dimensional constants are dimensionless.
Answer
(c) Dimensional constants are the quantities whose value are constant and they possesdimensions. For example, velocity of light in vacuum, universal gravitational constant, Boltzman constant, Planck's constant etc.
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Question 81 Mark
Assertion : When we change the unit of measurement of a quantity, its numerical value changes
Reason : smaller the unit of the measurement smaller is its numerical value.
Answer
(c) We know that $Q=n_1 u_1=n_2 u_2$ are the two units of measurement of the quantity $Q$ and $n, n$ are their respective numerical values. From relation $Q_1=n_1 u_1=n_2 u_2, nu=$ constant $\Rightarrow n \propto 1 / u$ i.e., smaller the unit of measurement, greateris its numerical value.
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Question 91 Mark
Assertion : A.U. is much bigger than $\mathring A$.
Reason : A.U. stands for astronomical unit and $\mathring A$ stands from Angstrom.
Answer
(b) A.U. is used (Astronomical units) to measure the average distance of the centre of thesun from the centre of the earth, while angstrom is used for very short distances. 1 A.U. = $1.5\times 10^{11} \mathrm{~m} ; 1 . \hat{A}=10^{-10} \mathrm{~m}$.
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Question 101 Mark
Assertion $\quad:$ Radian is the unit of distance.
Reason : One radian is the angle subtended at the centre of a circle by an arc equal in length to the radius of the circle.
Answer
(e) Radian is the unit of plane angle.
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Question 111 Mark
Assertion $\quad: \ln y=A \sin (\omega t-k x),(\omega t-k x)$ is dimensionless.
Reason $\quad:$ Because dimension of $\omega=\left[M^0 L^0 T\right]$.
Answer
(c) As $\omega$ (angular velocity) has the dimension of $\left[T^{-1}\right]$ not $[T$.
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Question 121 Mark
Assertion : surface tension and surface energy have the same dimensions.
Reason : Because both have the same S.I. unit
Answer
(c) As surface tension and surface energy both have different S.l. unit and same dimensional formula.
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Question 131 Mark
Assertion : Radar is used to detect an aeroplane in the sky
Reason : Radar works on the principle of reflection of waves.
Answer
(a) As radar is most accurate instrument used to detect aeroplane in sky based on principle of reflection of radio waves.
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Question 141 Mark
Assertion : Now a days a standard metre is defined as in terms of the wavelength of light.
Reason : Light has no relation with length.
Answer
(c) Because representation of standard metre in terms of wavelength of light is most accurate.
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Question 151 Mark
Assertion : Density is a derived physical quantity.
Reason : Density cannot be derived from the fundamental physical quantities.
Answer
(c) Because density can be derived from fundamental quantities.
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Question 161 Mark
Assertion : Mass, length and time are fundamental physical quantities.
Reason : They are independent of each other.
Answer
(a) As length, mass and time represent our basic scientific notations, therefore they are called fundamental quantities and they cannot be obtained from each other.
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Question 171 Mark
Assertion : Out of three measurements $I=0.7 m$; $=0.70 m$ and $I=0.700 m$, the last one is most accurate.
Reason : In every measurement, only the last significant digit is not accurately known.
Answer
(b) The last number is most accurate because it has greatest significant figure (3).
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Question 181 Mark
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.
Answer
(c) Since zeros placed to the left of the number are never significant, but zeros placed to right of the number are significant.
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Question 191 Mark
Assertion : Parallex method cannot be used for measuring distances of stars more than 100 light years away.
Reason : Because parallex angle reduces so much that it cannot be measured accurately.
Answer
(a) As the distance of star increases, the parallax angle decreases, and great degreeofaccuracy is required for its measurement. Keeping in view the practical limitation imeasuring the parallax angle, the maximum distance of a star we can measure is limited to100 light year.
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Question 201 Mark
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.
Answer
(a)
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Question 211 Mark
Assertion : Rate of flow of a liquid represents velocity of flow.
Reason : The dimensions of rate of flow are $[M L T]$.
Answer
(d) Rate of flow of liquid is expressed as the volume of liquid flowing per second and it has dimension $\left[L^3 T^{-1}\right]$.
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Question 221 Mark
Assertion : Linear mass density has the dimensions of $[M L T]$.
Reason : Because density is always mass per unit volume.
Answer
(c) Density is not always mass per unit volume.
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Question 231 Mark
Assertion : Force cannot be added to pressure.
Reason : Because their dimensions are different.
Answer
(a) Addition and subtraction can be done between quantities having same dimension.
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Question 241 Mark
Assertion : Light year and year, both measure time.
Reason : Because light year is the time that light takes to reach the earth from the sun.
Answer
(d) Light year measures distance and year measures time. One light year is the distance traveled by light in one year.
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Question 251 Mark
Assertion : 'Light year' and 'Wavelenght' both measure distance.
Reason : Both have dimensions of time. 
Answer
(c) Light year and wavelength both represents the distance, so both has dimension of length not of time.
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Assertion & Reason - JEE physics STD 12 Science Questions - Vidyadip