CBSE Questions for Class 11 Engineering Physics Units And Measurement Quiz 11 - MCQExams.com

Multiple Correct Answers Type
Which of the following pairs has the same dimensions?
  • Torque and work
  • Angular momentum and Planck's constant
  • Energy and Young's modulus
  • Light year and wave length
A vernier callipers has its main scale of $$10 cm$$ equally divided into $$200$$ equal parts. Its vernier scale of $$25$$ divisions coincides with $$12 mm$$ on the main scale. The least count of the instrument is - 
  • $$0.020 cm$$
  • $$0.002 cm$$
  • $$0.010 cm$$
  • $$0.001 cm$$
The potential energy of a particle varies with distance $$x$$ as $$U = \dfrac{Ax^{1/2}}{x^2 + B}$$, where A and B are constants. The dimensional formula for A x B is:
  • $$M^1L^{7/2}T^{-2}$$
  • $$M^1L^{11/4}T^{-2}$$
  • $$M^1L^{5/2}T^{-2}$$
  • $$M^1L^{9/2}T^{-2}$$
In terms of resistance $$R$$ and time $$T$$, the dimensions of ratio $$\dfrac {\mu}{\epsilon}$$ of the permeability $$\mu$$ and permittivity $$\epsilon$$ is:
  • $$[R^{2}T^{2}]$$
  • $$[RT^{-2}]$$
  • $$[R^{2}T^{-1}]$$
  • $$[R^{2}]$$
Match the physical quantities given in Column I with dimensions expressed in terms of mass (M), length (L) time (T), and charge (Q) given in Column II.
Column IColumn II
i. Angular momentuma. $$ML^2T^{-2}$$
ii. Torqueb. $$ML^2T^{-1}$$
iii. Inductancec. $$M^{-1}L^{-2}T^2Q^2$$
iv. Latent heatd. $$ML^2Q^{-2}$$
v. Capacitancee. $$ML^3T^{-1}Q^{-2}$$
vi. Resistivityf. $$L^2T^{-2}$$
  • $$i \rightarrow c., ii \rightarrow a., iii \rightarrow d., iv \rightarrow f., v \rightarrow b., vi \rightarrow e$$
  • $$i \rightarrow b., ii \rightarrow a., iii \rightarrow d., iv \rightarrow f., v \rightarrow c., vi \rightarrow e$$
  • $$i \rightarrow b., ii \rightarrow e., iii \rightarrow d., iv \rightarrow f., v \rightarrow c., vi \rightarrow a$$
  • $$i \rightarrow b., ii \rightarrow a., iii \rightarrow f., iv \rightarrow d., v \rightarrow c., vi \rightarrow e$$
Multiple Correct Answers Type
Which of the following pairs have different dimensions?
  • Frequency and angular velocity
  • Tension and surface tension
  • Density and energy density.
  • Linear momentum and angular momentum.
The dimension of electrical conductivity is _________.
  • $$M^{-2}L^{-4}T^3A^2$$.
  • $$M^{-1}L^{-2}T^3A^2$$.
  • $$M^{-1}L^{-3}T^4A^2$$.
  • $$M^{-2}L^{-3}T^6A^2$$.
The dimension of permittivity of vacuum 
  • $$[M^{ -2} L^ {-3} T^4 A^2]$$
  • $$[M^{ -1} L^ {-3} T^4 A^3]$$
  • $$[M^{ -1} L^ {-3} T^4 A^2]$$
  • $$ [M^{ -1} L^ {-5} T^4 A^2]$$
Dimensions of $$\dfrac {1}{\mu_{0}\epsilon_{0}}$$, where symbols have their usual meaning, are:
  • $$[L^{-1}T]$$
  • $$[L^{-2}T^{2}]$$
  • $$[L^{2}T^{-2}]$$
  • $$[LT^{-1}]$$
The dimension of magnetic field in $$M, L, T$$ and $$C$$ (Coulomb) is given as:
  • $$MLT^{-1}C^{-1}$$
  • $$MT^{2}C^{-2}$$
  • $$MT^{-1}C^{-1}$$
  • $$MLT^{-2}C^{-1}$$
A metal sample carrying a current along $$X-$$axis with density $$J_{x}$$ is subjected to a magnetic field $$B_{z}$$ (along $$z-$$axis). The electric field $$E_{y}$$ developed along $$Y-$$axis is directly proportional to $$J_{x}$$ as well as $$B_{z}$$. The constant of proportionality has $$SI$$ unit.
  • $$\dfrac{m^{2}}{A}$$
  • $$\dfrac{m^{3}}{As}$$
  • $$\dfrac{m^{2}}{As}$$
  • $$\dfrac{As}{m^{3}}$$
Two particles of mass $${m}_{1}$$ and $${m}_{2}$$ are approaching towards each other under their mutual gravitational field. If the speed of the particle is $$v$$, the speed of the center of mass of the system is equal to:
  • $$\cfrac { { m }_{ 1 } }{ { m }_{ 2 } } v$$
  • zero
  • $$\cfrac { \left( { m }_{ 1 }-{ m }_{ 2 } \right) v }{ { m }_{ 1 }+{ m }_{ 2 } } $$
  • $$\cfrac { { m }_{ 2 } }{ { m }_{ 1 } } v$$
Give the MKS units for the following quantities.
Power of lens.
  • hertz
  • Dioptre.
  • ohms
  • unit less
In the formula $$X=3YZ^2$$, X and Z have dimensions of capacitance and magnetic induction respectively. The dimensions of Y in MKSQ system are ________.
  • $$-2$$ in mass, $$-2$$ in length, $$4$$ in time and $$5$$ in charge.
  • $$-3$$ in mass, $$-2$$ in length, $$4$$ in time and $$4$$ in charge.
  • $$-4$$ in mass, $$-5$$ in length, $$4$$ in time and $$4$$ in charge.
  • $$-3$$ in mass, $$-2$$ in length, $$8$$ in time and $$7$$ in charge.
Planck's constant has the dimensions ___________.
  • $$ML^3T^{-1}$$.
  • $$ML^2T^{-1}$$.
  • $$ML^6T^{-1}$$.
  • $$ML^8T^{-1}$$.
The dimensions of angular momentum, latent heat and capacitance are, respectively.
  • $$ML^{2}T^{1}A^{2}, L^{2}T^{-2}M^{-1}L^{-2}T^{2}$$
  • $$MLT^{2}, L^{2}T^{2}, M^{-1}L^{-2}T^{4}A^{2}$$
  • $$ML^{2}T^{-1}, L^{2}T^{-2}, ML^{2}TA^{2}$$
  • $$ML^{2}T^{-1}, L^{2}T^{-2}, M^{-1}L^{-2}T^{4}A^{2}$$
The physical quantities which do not have same dimensions are
  • Energy and Torque
  • Pressure and Stress
  • Work and Energy
  • Strain and Youngs Modulus
Two particles X and Y having equal charges, after being accelerated through the same potential difference, enter a region of uniform magnetic field and describe circular paths of radii $$R_1$$and $$R_2$$, respectively. The ratio of the masses of  X to that of Y is
  • $$(R_1/R_2)^{1/2}$$
  • $$R_2/R_1$$
  • $$(R_1/R_2)^2$$
  • $$R_1/R_2$$
The equation of the state of some gases can be expressed as $$(P + \dfrac{a}{V^2} = \dfrac{R\theta}{V})$$, where P is the pressure. V the volume, $$\theta$$ the absolute temperature and a and b are constant. The dimensional formula of a is  
  • $$[ML^5T^{-2}]$$
  • $$[M^{-1}L^5T^{-2}]$$
  • $$[ML^{-1}T^{-2}]$$
  • $$[ML^{-5}T^{-2}]$$
If $$y$$ represents pressure and $$x$$ represents velocity  gradient, then the dimensions of $$\dfrac { { d }^{ 2 }y }{ d{ x  }^{ 2 } }$$ are
  • $$\left[ ML^{ -1 }T^{ -2 } \right] $$
  • $$\left[ M^{2}L^{ -2 }T^{ -2 } \right] $$
  • $$\left[ ML^{ -1 }T^{ 0 } \right] $$
  • $$\left[ M^{2}L^{ -2 }T^{ -4 } \right] $$
Dimensional equation of universal constant of gravitation is:
  • $$
    \left[ {M^0 L^1 T^2 } \right]
    $$
  • $$
    \left[ {M^1 L^{ - 3} T^{ - 2} } \right]
    $$
  • $$
    \left[ {M^{ - 1} L^3 T^{ - 2} } \right]
    $$
  • $$
    \left[ {M^{ - 1} L^3 T^2 } \right]
    $$
The dimensions of planck's constant equal to that of 
  • energy
  • momentum
  • angular momentum
  • power
In the formula : y = a sin ( at - b), where y - position, t - time and A, a, b are constants. What will be the dimensional formula of $$\frac{b}{a}$$?
  • T
  • L
  • $$L^{-1}$$
  • $$T^{-1}$$
The radius of a sphere is $$(2.6 \pm 0.1)$$ cm. The percentage error in its volume is
  • $$\dfrac{0.1}{2.6} \times 100% $$
  • $$ 3 \times \dfrac{0.1}{2.6} \times 100% $$
  • $$ \dfrac{{8.49}}{{73.6}} \times 100$$
  • $$\dfrac{0.1}{2.6} % $$
The dimensions of emf in MKS is:
  • $${ML^{-1}}{T^{-2}}{Q^{-2}}$$
  • $${ML^{2}}{T^{-2}}{Q^{-2}}$$
  • $${MLT^{-2}}{Q^{-1}}$$
  • $${ML^{2}}{T^{-2}}{Q^{-1}}$$
The dimension of $$\left( \dfrac { 1 }{ 2 }  \right) { \varepsilon  }_{ 0 }{ E }^{ 2 }$$ is($${ \varepsilon  }_{ 0 }$$: permittivity of free space, Electric field)
  • $${ MLT }^{ -1 }$$
  • $${ ML }^{ 2 }{ T }^{ -2 }$$
  • $${ ML }^{ -1 }{ T }^{ -2 }$$
  • $${ ML }^{ 2 }{ T }^{ -1 }$$
The velocity of a body moving viscous medium is given by $$V=\dfrac { A }{ B } [1-{ e }^{ { -t }/{ B } }]$$ where $$t$$ is time, $$A$$ and $$B$$ are constants. Then the dimensional formula of $$A$$ is:
  • $${ M }^{ 0 }{ L }^{ 0 }{ T }^{ 0 }$$
  • $${ M }^{ 0 }{ L }^{ 1 }{ T }^{ 0 }$$
  • $${ M }^{ 0 }{ L }^{ 1 }{ T }^{ -1 }$$
  • $${ M }^{ 1 }{ L }^{ 1 }{ T }^{ -1 }$$
Write down the significant figures in the following
$$5238$$ N
$$4200 $$kg
  • $$4 , 4$$
  • $$4 , 2$$
  • $$4, 3$$
  • $$5, 3$$

The dimension of the magnetic field intensity B is  
  • $$(a)\,ML{T^{ - 2\,}}\,{A^{ - 1}}$$
  • $$(b)\,M{T^{ - 2\,}}\,{A^{ - 1}}$$
  • $$(c)\,M{L^{2\,}}\,T{A^{ - 2}}$$
  • $$(d)\,{M^{2\,\,}}L{T^{ - 2}}\,{A^{ - 1}}$$
In the context of accuracy to measurement and significant figures in expressing results of experiment, which of the following is/are correct?
(1) Out of the measurements 50.14 cm and 0.00025 ampere, the first one has greater accuracy.
(2) If one travels 478 km by rail and 397 m. by road, the total distance traveled is 478 km.
  • Only (1) is correct
  • Only (2) is correct
  • Both are correct
  • None of these is correct.
Dimension of $$\epsilon_0$$ are
  • $$ [M^0 L^0 T^0 A^0 ] $$
  • $$ [M^0 L^{-3} T^3 A^3 ] $$
  • $$ [M^{-1} L^{-3} T^3 A^1 ] $$
  • $$ [M^{-1} L^{-3} T^4 A^2 ] $$
Which of the following is dimensionally incorrect ?
  • $$u=v-at$$
  • $$s-ut=\dfrac{1}{2}at^2$$
  • $$u^2=2a(gt-1)$$
  • $$v^2-u^2=2as$$
The dimensions of energy per unit volumes are the same as those of :
  • Work
  • Stress
  • Pressure
  • Modulus
Pressure P varies as $$P=\cfrac { \alpha  }{ \beta  } exp\left( \cfrac { -\alpha  }{ { K }_{ B }\theta  } Z \right) $$ where Z denotes distance. $${ K }_{ B }$$ Boltzman's constant.$$\theta $$ temperature and $$\alpha ,\beta$$ are constants.Derive the dimensions of $$\beta $$
  • $$\left[ { M }^{ -1 }{ LT }^{ -2 } \right] $$
  • $$\left[ { M }^{ 0 }{ L }^{ 0 }{ T }^{ 0 } \right] $$
  • $$\left[ { M }^{ 0 }{ L }^{ 2 }{ T }^{ 0 } \right] $$
  • $$\left[ { M }^{ 0 }{ L }^{ -1 }{ T }^{ -2 } \right] $$
The dimensional formula of angular velocity $$\left(\omega=\cfrac{v}{r}\right)$$ is
  • $$ML^oT^{-2}$$
  • $$MLT^{-1}$$
  • $$M^0L^0T^{-1}$$
  • $$ML^oT^{1}$$
The dimension of combination $$\dfrac{L}{CVR}$$ are same as dimensions of 
  • Change
  • Current
  • Charge$$^{-1}$$
  • Current $$^{-1}$$
Pressure P varies as $$P=\dfrac{\alpha}{\beta}$$ exp$$(\dfrac{-\alpha}{K_B \theta}Z)$$ where Z denotes distance,$$K_B$$ Boltzman's constant,$$\theta$$ absolute temperature and $$\alpha,\beta$$ are constants.Derive the dimensions of $$\beta$$
  • $$[M^{-1} L T^{-2}]$$
  • $$[M^0 L^0 T^0]$$
  • $$[M^0 L^2 T^0]$$
  • $$[M^0 L^{-1} T^{-2}]$$
If temperature of sun is decreased by $$1\%$$ then the value of solar constant will change by
  • $$2\%$$
  • $$-4\%$$
  • $$-2\%$$
  • $$4\%$$
A dimensionless quantity :
  • may have a unit
  • never has a unit
  • always has a unit
  • does not exist
If the dimension of a physical quantity is given by $$[M^aL^bT^c]$$ then the physical quantity will be
  • acceleration, if a = 1, b =-1, c =-2
  • velocity, if a = 1, b =0, c =-1
  • pressure, if a = 1, b =-1, c =-2
  • force, if a = 0, b =-1, c =-2
The equation of state of some gases can be expressed as $$\left(P+\dfrac{a}{V^{2}}\right)\left(V-b\right)=RT$$. Here P is the pressure, $$V$$ is the volume, $$T$$ is the absolute temperature and $$a,b,R$$ are constant. The dimensions of $$a$$ are:
  • $$ML^{5}T^{-2}$$
  • $$ML^{-1}T^{-2}$$
  • $$M^{0}L^{3}T^{0}$$
  • $$M^{0}L^{6}T^{0}$$
If there is a positive error of $$50\%$$ in the measurement of velocity of a body, then the error in the measurement of kinetic energy is :
  • $$25\%$$
  • $$50\%$$
  • $$100\%$$
  • $$125\%$$
Choose the incorrect statements out of the following:-
  • Every measurement by any measuring instrument has some errors
  • Every calculated physical quantity that is based on measured values has some error
  • A measurement can have more accuracy but less precision and vice-versa
  • The percentage error is different from relative error.
A student uses a metre scale, measuring upto $$1\ mm$$, to measure the length an breadth of a retangular plate. He finds that length$$=5.7\ cm$$ and breadth $$=3.4\ cm$$. What is the percentage error in the area of the plate?
  • $$3.58\%$$
  • $$4.7\%$$
  • $$5.3\%$$
  • $$6.2\%$$
The dimensional formula for thermal resistance is
  • $$\left [ ML^{2}T^{-3}K^{-1} \right ]$$
  • $$\left [ ML^{2}T^{-2}A^{-1} \right ]$$
  • $$\left [ ML^{2}T^{-3}K^{-2} \right ]$$
  • $$\left [ M^{-1}L^{-2}T^{3}K \right ]$$
Find the dimensions of inductance
  • $$ML^{2}T^{-2}A^{-2}$$
  • $$ML^{2}T^{-1}A^{-1}$$
  • $$MLT^{-1}A^{-1}$$
  • $$MLTA^{-2}$$
The dimension formula of torque is 
  • $$M{L^2}$$
  • $$MLT$$
  • $$MLT^2$$
  • $$ML^2T^{-2}$$
Find the maximum possible percentage error in the measurement of force on an object(on mass m) travelling at velocity v in a circle of radius r, if m=(4.0 plus minus 0.1)kg, v=(10 plus minus 0.1)m/s and r=(8.0 plus minus 0.2)m
  • ( 50 ± 1) N
  • ( 50 ± 2.5) N
  • ( 50 ± 1.5) N
  • ( 50 ± 3.5) N
A physical quantity $$P$$ is given by the relation, $$P={P}_{0}{e}^{(-\alpha {t}^{2})}$$. If $$t$$ denotes the time, the dimensions of constant $$\alpha$$ are
  • $$[T]$$
  • $$[{T}^{2}]$$
  • $$[{T}^{-1}]$$
  • $$[{T}^{-2}]$$
if $$L=2.331 cm$$, $$B = 2.1 cm$$, then L+B=
  • $$4.431cm$$
  • $$4.43cm$$
  • $$4.5cm$$
  • $$4.2cm$$
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