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JEE physics MCQ

Units, Dimensions and Measurement · CBSE STD 12 Science (CBSE - English Medium). 293 questions.

Questions · Page 2 of 6

MCQ

MCQ 511 Mark
One yard in Sl units is equal
  • A
    1.9144 metre
  • ✓
    0.9144 metre
  • C
    0.09144 kilometre
  • D
    1.0936 kilometre
Answer
Correct option: B.
0.9144 metre
(b) 1 yard $=36$ inches $=36 \times 2.54 \mathrm{~cm}=0.9144 \mathrm{~m}$.
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MCQ 521 Mark
The dimensions of surface tension are
  • A
    $M L^{-1} T^{-2}$
  • B
    $M L T^{-2}$
  • C
    $M L^{-1} T^{-1}$
  • ✓
    $M T^{-2}$
Answer
Correct option: D.
$M T^{-2}$
(d) Surface tension $=\frac{\text { Force }}{\text { Length }}=\frac{\left[M L T^{-2}\right]}{L}=\left[M T^{-2}\right]$
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MCQ 531 Mark
Young's modulus of a material has the same units as
  • ✓
    Pressure
  • B
    Strain
  • C
    Compressibility
  • D
    Force
Answer
Correct option: A.
Pressure
(a) $\quad Y=\frac{\text { Stress }}{\text { Strain }}=\frac{\text { Force/Area }}{\text { Dimensionless }} \Rightarrow Y \equiv$ Pressure.
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MCQ 541 Mark
The dimensions of coefficient of thermal conductivity is
  • A
    $M L^2 T^{-2} K^{-1}$
  • ✓
    $M L T^{-3} K^{-1}$
  • C
    $M L T^{-2} K^{-1}$
  • D
    $M L T^{-3} K$
Answer
Correct option: B.
$M L T^{-3} K^{-1}$
(b$\frac{d Q}{d t}=-K A\left(\frac{d \theta}{d x}\right)$
$\Rightarrow[K]=\frac{\left[M L^2 T^{-2}\right]}{[T]} \times \frac{[L]}{\left[L^2\right][K]}=M L T^{-3} K^{-1}$
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MCQ 551 Mark
The equation of a wave is given by $Y=A \sin \omega\left(\frac{x}{v}-k\right)$ where $\omega$ is the angular velocity and $v$ is the linear velocity. The dimension of $k$ is
  • A
    $L T$
  • ✓
    $T$
  • C
    $T^{-1}$
  • D
    $T^2$
Answer
Correct option: B.
$T$
(b) From the principle of homogenity $\left(\frac{x}{v}\right)$ has dimensions of $T$.
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MCQ 561 Mark
Electron volt is a unit of
  • A
    Charge
  • B
    Potential difference
  • C
    Momentum
  • ✓
    Energy
Answer
Correct option: D.
Energy
(d)
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MCQ 571 Mark
$\ln S=a+b t+c t^2 . S$ is measured in metres and $t$ in seconds. The unit of $c$ is
  • A
    None
  • B
    $m$
  • C
    $m s^{-1}$
  • ✓
    $ms ^{-2}$
Answer
Correct option: D.
$ms ^{-2}$
(d) $c t^2$ must have dimensions of $L$$\Rightarrow c$ must have dimensions of $L / T^2$ i.e. $L T^{-2}$.
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MCQ 581 Mark
Dimensional formula for volume elasticity is
  • A
    $M^1 L^{-2} T^{-2}$
  • B
    $M^1 L^{-3} T^{-2}$
  • C
    $M^1 L^2 T^{-2}$
  • ✓
    $M^1 L^{-1} T^{-2}$
Answer
Correct option: D.
$M^1 L^{-1} T^{-2}$
(d) Volume elasticity $=\frac{\text { Force } / \text { Area }}{\text { Volume strain }$Strain is dimensionless, so=\frac{\text { Force }}{\text { Area }}=\frac{M L T^{-2}}{L^2}=\left[M L^{-1} T^{-2}\right]$
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MCQ 591 Mark
Light year is a unit of
  • A
    Time
  • B
    Mass
  • ✓
    Distance
  • D
    Energy
Answer
Correct option: C.
Distance
(c) Light year is a distance which light travels in one year
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MCQ 601 Mark
Unit of Stefan's constant is
  • A
    $J s^{-1}$
  • ✓
    $J m^{-2} s^{-1} K^{-4}$
  • C
    $J m^{-2}$
  • D
    $J s$
Answer
Correct option: B.
$J m^{-2} s^{-1} K^{-4}$
(b) $\frac{Q}{t}=\sigma A T^4 \Rightarrow \sigma=J m^{-2} s^{-1} K^{-4}$
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MCQ 611 Mark
The unit of surface tension in $Sl$ system is
  • A
    Dyne $/ cm ^2$
  • ✓
    Newton / m
  • C
    Dyne / cm
  • D
    Newton $/ m^2$
Answer
Correct option: B.
Newton / m
(b) Surface tension $=\frac{\text { Force }}{\text { Length }}=$ Newtons $/$ metre
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MCQ 621 Mark
Unit of stress is
  • A
    $N / m$
  • B
    $N-m$
  • ✓
    $N / m ^2$
  • D
    $N \rightarrow m^2$
Answer
Correct option: C.
$N / m ^2$
(c) Stress $=\frac{\text { Force }}{\text { Area }}=\frac{N}{m^2}$
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MCQ 631 Mark
Unit of moment of inertia in MKS system
  • A
    $kg \times cm ^2$
  • B
    $kg / cm ^2$
  • ✓
    $kg \times m ^2$
  • D
    Joule $\times m$
Answer
Correct option: C.
$kg \times m ^2$
(c) As $I=M R^2=k g-m^2$
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MCQ 641 Mark
The unit of self inductance of a coil is
  • A
    Farad
  • ✓
    Henry
  • C
    Weber
  • D
    Tesla
Answer
Correct option: B.
Henry
(b) $L=\frac{\phi}{I}=\frac{W b}{A}=$ Henry.
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MCQ 651 Mark
Out of the following, the only pair that does not have identical dimensions is
  • A
    Angular momentum and Planck's constant
  • ✓
    Moment of inertia and moment of a force
  • C
    Work and torque
  • D
    Impulse and momentum
Answer
Correct option: B.
Moment of inertia and moment of a force
(b)$\begin{array}{l\text { Moment of inertia }=m r^2=[M]\left[L^2\right] \\\text { Moment ofForce }=\text { Force } \times \text { Perpendicular distance } \\=\left[M L T^{-2}\right][L]=\left[M L^2 T^{-2}\right]\end{array}$
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MCQ 661 Mark
The dimension of $\frac{R}{L}$ are
  • A
    $T^2$
  • B
    $T$
  • ✓
    $T^{-1}$
  • D
    $T^{-2}$
Answer
Correct option: C.
$T^{-1}$
(c) $L / R$ is a time constant so $(R / L)=T^{-1}$
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MCQ 671 Mark
Dimensions of potential energy are
  • A
    $M L T^{-1}$
  • ✓
    $M L^2 T^{-2}$
  • C
    $M L^{-1} T^{-2}$
  • D
    $M L^{-1} T^{-1}$
Answer
Correct option: B.
$M L^2 T^{-2}$
(b)
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MCQ 701 Mark
The dimensional formula for Boltzmann's constant is
  • ✓
    $\left[M L^2 T^{-2} \theta^{-1}\right]$
  • B
    $\left[M L^2 T^{-2}\right]$
  • C
    $\left[M L^0 T^{-2} \theta^{-1}\right]$
  • D
    $\left[M L^{-2} T^{-1} \theta^{-1}\right]$
Answer
Correct option: A.
$\left[M L^2 T^{-2} \theta^{-1}\right]$
(a) $k=\left[\frac{R}{N}\right]=\left[M L^2 T^{-2} \theta^{-1}\right]$
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MCQ 711 Mark
Which of the following quantities is dimensionless
  • A
    Gravitational constant
  • B
    Planck's constant
  • C
    Power of a convex lens
  • ✓
    None
Answer
Correct option: D.
None
(d)$G]=\left[M^{-1} L^3 T^{-2}\right] ;[h]=\left[M L^2 T^{-1}\right]$Power $=\frac{1}{\text { focal length }}=\left[L^{-1}\right]$All quantities have dimensions
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MCQ 721 Mark
Which of the following is not the unit of energy
  • A
    Calorie
  • B
    Joule
  • C
    Electron volt
  • ✓
    Watt
Answer
Correct option: D.
Watt
(d) Watt is a unit of power
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MCQ 731 Mark
The dimensions of permittivity $\varepsilon_0$ are
  • A
    $A^2 T^2 M^{-1} L^{-3}$
  • ✓
    $A^2 T^4 M^{-1} L^{-3}$
  • C
    $A^{-2} T^{-4} M L^3$
  • D
    $A^2 T^{-4} M^{-1} L^{-3}$
Answer
Correct option: B.
$A^2 T^4 M^{-1} L^{-3}$
(b)$F=\frac{1}{4 \pi \varepsilon_0} \frac{q_1 q_2}{r^2}$
$\Rightarrow \varepsilon_0=\frac{\left|q_1\right|\left|q_2\right|}{[F]\left[r^2\right]}=\frac{\left[A^2 T^2\right]}{\left[M L T^{-2}\right]\left[L^2\right]}=\left[A^2 T^4 M^{-1} L^{-3}\right]$
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MCQ 741 Mark
Dimensions of the following three quantities are the same
  • A
    Work, energy, force
  • B
    Velocity, momentum, impulse
  • C
    Potential energy, kinetic energy, momentum
  • ✓
    Pressure, stress, coefficient of elasticity
Answer
Correct option: D.
Pressure, stress, coefficient of elasticity
(d) $[$ Pressure $]=[$ Stress $]=[$ coefficient of elasticity $]=\left[M L^{-1} T^{-2}\right]$
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MCQ 751 Mark
The pair having the same dimensions is
  • A
    Angular momentum, work
  • ✓
    Work, torque
  • C
    Potential energy, linear momentum
  • D
    Kinetic energy, velocity
Answer
Correct option: B.
Work, torque
(b) Dimension of work and torque $=\left[M L^2 T^{-2}\right]$
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MCQ 761 Mark
Temperature can be expressed as a derived quantity in terms of any of the following
  • A
    Length and mass
  • B
    Mass and time
  • C
    Length, mass and time
  • ✓
    None of these
Answer
Correct option: D.
None of these
(d) Because temperature is a fundamental quantity.
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MCQ 771 Mark
The dimensions of "time constant" $\frac{L}{R}$ during growth and decay of current in all inductive circuit is same as that of
  • A
    Constant
  • B
    Resistance
  • C
    Current
  • ✓
    Time
Answer
Correct option: D.
Time
(d) $\frac{L}{R}=$ Time constant.
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MCQ 781 Mark
The dimensions of resistivity in terms of $M, L, T$ and $Q$ where $Q$ stand for the dimensions of charge, is
  • ✓
    $M L^3 T^{-1} Q^{-2}$
  • B
    $M L^3 T^{-2} Q^{-1}$
  • C
    $M L^2 T^{-1} Q^{-1}$
  • D
    $M L T^{-1} Q^{-1}$
Answer
Correct option: A.
$M L^3 T^{-1} Q^{-2}$
(a) $\rho=\frac{R A}{l}$ i.e. dimension of resistivity is $\left[M L^3 T^{-1} Q^{-2}\right]$
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MCQ 791 Mark
The dimensions of Farad are
  • ✓
    $M^{-1} L^{-2} T^2 Q^2$
  • B
    $M^{-1} L^{-2} T Q$
  • C
    $M^{-1} L^{-2} T^{-2} Q$
  • D
    $M^{-1} L^{-2} T Q^2$
Answer
Correct option: A.
$M^{-1} L^{-2} T^2 Q^2$
(a) Farad is the unit of capacitance and $C=\frac{Q}{V}=\frac{[Q]}{\left[M L^2 T^{-2} Q^{-1}\right]}=M^{-1} L^{-2} T^2 Q^2$
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MCQ 801 Mark
The dimensions of stress are equal to
  • A
    Force
  • ✓
    Pressure
  • C
    Work
  • D
    $\frac{1}{\text { Pressure }}$
Answer
Correct option: B.
Pressure
(b) $[$ Pressure $]=[$ stress $]=\left[M L^{-1} T^{-2}\right]$
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MCQ 811 Mark
Unit of magnetic moment is
  • ✓
    Ampere-metre ${ }^2$
  • B
    Ampere-metre
  • C
    Weber-metre ${ }^2$
  • D
    Weber/metre
Answer
Correct option: A.
Ampere-metre ${ }^2$
(a) $M=$ Pole strength $\times$ length $=$ amp-metre $\times$ metre $=$ amp-metr $e^2$
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MCQ 821 Mark
Dimensions of strain are
  • A
    $M L T^{-1}$
  • B
    $M L^2 T^{-1}$
  • C
    $M L T^{-2}$
  • ✓
    $M^0 L^0 T^0$
Answer
Correct option: D.
$M^0 L^0 T^0$
(d) Strain is dimensionless.
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MCQ 831 Mark
In Sl, Henry is the unit of
  • A
    Self inductance
  • B
    Mutual inductance
  • ✓
    and both
  • D
    None of the above
Answer
Correct option: C.
and both
(c)
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MCQ 841 Mark
Unit of self inductance is
  • A
    $\frac{\text { Newton -second }}{\text { Coulomb } \times \text { Ampere }}$
  • ✓
    $\frac{\text { Joule/Coulomb } \times \text { Second }}{\text { Ampere }}$
  • C
    $\frac{\text { Volt } \times \text { metre }}{\text { Coulomb }}$
  • D
    $\frac{\text { Newton } \times \text { metre }}{\text { Ampere }}$
Answer
Correct option: B.
$\frac{\text { Joule/Coulomb } \times \text { Second }}{\text { Ampere }}$
(b)
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MCQ 851 Mark
The equation $\left(P+\frac{a}{V^2}\right)(V-b)$ constant. The units of $a$ are
  • A
    Dyne $\times cm ^5$
  • ✓
    Dyne $\times cm ^4$
  • C
    Dyne $/ cm ^3$
  • D
    Dyne/cm
Answer
Correct option: B.
Dyne $\times cm ^4$
(b) Units of $a$ and $P V$ are same and equal to $d y n e \times c m$.
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MCQ 861 Mark
A suitable unit for gravitational constant is
  • A
    $k g-m sec ^{-1}$
  • B
    $N m^{-1} sec$
  • ✓
    $N m^2 kg ^{-2}$
  • D
    $k g m sec ^{-1}$
Answer
Correct option: C.
$N m^2 kg ^{-2}$
(c) $F=\frac{G m_1 m_2}{d^2} ; \therefore G=\frac{F d^2}{m_1 m_2}=\mathrm{Nm}^2 / \mathrm{kg}^2$
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MCQ 871 Mark
One second is equal to
  • A
    1650763.73 time periods of $K r$ clock
  • B
    652189.63 time periods of $K r$ clock
  • C
    1650763.73 time periods of $C s$ clock
  • ✓
    9192631770 time periods of Cs clock
Answer
Correct option: D.
9192631770 time periods of Cs clock
(d) lt is by standard definition.
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MCQ 881 Mark
How many wavelength of $K r^{86}$ are there in one metre
  • A
    1553164.13
  • ✓
    1650763.73
  • C
    652189.63
  • D
    2348123.73
Answer
Correct option: B.
1650763.73
(b) According to the definition.
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MCQ 891 Mark
The dimensional formula for the modulus of rigidity is
  • A
    $M L^2 T^{-2}$
  • B
    $M L^{-1} T^{-3}$
  • C
    $M L^{-2} T^{-2}$
  • ✓
    $M L^{-1} T^{-2}$
Answer
Correct option: D.
$M L^{-1} T^{-2}$
(d) Modulus of rigidity $=\frac{\text { Shear stress }}{\text { Shear strain }}=\left[M L^{-1} T^{-2}\right]$
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MCQ 901 Mark
Hertz is the unit for
  • ✓
    Frequency
  • B
    Force
  • C
    Electric charge
  • D
    Magnetic flux
Answer
Correct option: A.
Frequency
(a)
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MCQ 911 Mark
In the following list, the only pair which have different dimensions, is
  • ✓
    Linear momentum and moment of a force
  • B
    Planck's constant and angular momentum
  • C
    Pressure and modulus of elasticity
  • D
    Torque and potential energy
Answer
Correct option: A.
Linear momentum and moment of a force
(a) Linear momentum $=$ Mass $\times$ Velocity $=\left[M L T^{-1}\right]$Moment of a force $=$ Force $\times$ Distance $=\left[M L^2 T^{-2}\right]$
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MCQ 921 Mark
Dimensional formula $M L^{-1} T^{-2}$ does not represent the physical quantity
  • A
    Young's modulus of elasticity
  • B
    Stress
  • ✓
    Strain
  • D
    Pressure
Answer
Correct option: C.
Strain
(c) Strain $=\frac{\Delta L}{L} \Rightarrow$ dimensionless quantity
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MCQ 931 Mark
If the unit of length and force be increased four times, then the unit of energy is
  • A
    Increased 4 times
  • B
    Increased 8 times
  • ✓
    Increased 16 times
  • D
    Decreased 16 times
Answer
Correct option: C.
Increased 16 times
(c) Energy $=$ force $\times$ distance, so if both are increased by 4 times then energy will increase by 16 times.
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MCQ 941 Mark
Which of the following system of units is not based on units of mass, length and time alone
  • ✓
    $Sl$
  • B
    MKS
  • C
    FPS
  • D
    CGS
Answer
Correct option: A.
$Sl$
(a) Because in S.l. system there are seven fundamental quantities.
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MCQ 951 Mark
A physical quantity $A$ is related to four observable $a, b, c$ 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 $A$
  • A
    $12 \%$
  • B
    $7 \%$
  • C
    $5 \%$
  • ✓
    $14 \%$
Answer
Correct option: D.
$14 \%$
(d) Percentage error in $A$
$=\left(2 \times 1+3 \times 3+1 \times 2+\frac{1}{2} \times 2\right) \%=14 \%$
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MCQ 961 Mark
If the acceleration due to gravity is $10 ms ^{-2}$ and the units of length and time are changed in kilometer and hour respectively, the numerical value of the acceleration is
  • A
    360000
  • B
    72000
  • C
    36000
  • ✓
    129600
Answer
Correct option: D.
129600
(d) $\begin{aligned} n_2 & =n_1\left[\frac{L_1}{L_2}\right]^1\left[\frac{T_1}{T_2}\right]^{-2}=10\left[\frac{\text { meter }}{k m}\right]^1\left[\frac{\mathrm{sec}}{h r}\right]^{-2} \\ n_2 & =10\left[\frac{m}{10^3 m}\right]^1\left[\frac{\mathrm{sec}}{3600 \mathrm{sec}}\right]^{-2}=129600\end{aligned}$
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MCQ 971 Mark
Out of following four dimensional quantities, which one quantity is to be called a dimensional constant
  • A
    Acceleration due to gravity
  • B
    Surface tension of water
  • C
    Weight of a standard kilogram mass
  • ✓
    The velocity of light in vacuum
Answer
Correct option: D.
The velocity of light in vacuum
(d)
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MCQ 981 Mark
Which one of the following is not a unit of young's modulus
  • ✓
    $N m^{-1}$
  • B
    $Nm ^{-2}$
  • C
    Dyne $cm ^{-2}$
  • D
    Mega Pascal
Answer
Correct option: A.
$N m^{-1}$
(a)
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MCQ 991 Mark
Density of a liquid in CGS system is $0.625 g / cm ^3$. What is its magnitude in Sl system
  • A
    0.625
  • B
    0.0625
  • C
    0.00625
  • ✓
    625
Answer
Correct option: D.
625
$\text { CGS SI } $
$ N_1 U_1=N_2 U-2 $
$N_1\left[M_1 L_1^{-3}\right]=N_2\left[M_2 L_2^{-3}\right] $
$ N_2=N_1\left[\frac{M_1}{M_2}\right] \times\left[\frac{L_1}{L_2}\right]^{-3}=0.625\left[\frac{1 \mathrm{~g}}{1 \mathrm{~kg}}\right] \times\left[\frac{1 \mathrm{~cm}}{1 \mathrm{~m}}\right]^{-3} $
$ =0.625 \times 10^{-3} \times 10^6=625$
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MCQ 1001 Mark
Sl unit of permittivity is
  • A
    $C^2 m^2 N^{-1}$
  • B
    $C^{-1} m^2 N^{-2}$
  • C
    $C^2 m^2 N^2$
  • ✓
    $C^2 m^{-2} N^{-1}$
Answer
Correct option: D.
$C^2 m^{-2} N^{-1}$
(d) $F=\frac{1}{4 \pi \in} \frac{q_1 q_2}{r^2} \Rightarrow \in=\frac{1}{4 \pi} \frac{q_1 q_2}{F r^2}=C^2 m^{-2} N^{-1}$
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