CBSE Questions for Class 11 Engineering Physics Units And Measurement Quiz 12 - MCQExams.com

The dimensional formula $$[ML^1T^{-3}]$$ is more closely associated with
  • power
  • energy
  • intensity
  • velocity gradient
A balloon of mass $$1$$ g has $$100$$ g of water in it. If it is completely immersed in water, its mass will be
  • $$0.5$$ g
  • $$1.2$$ g
  • $$1$$ g
  • $$1.5$$ g
Dimensional formula of self inductance is:
  • $$M L T^{-2} A^{-2}$$
  • $$M L^2 T^{-1} A^{-2}$$
  • $$M L^2 T^{-2} A^{-2}$$
  • $$M L^2 T^{-2} A^{-1}$$
While measuring $$g$$ using simple pendulum method $$\%$$ error in measurement of $$\ell$$ is $$\pm\ 2\%$$ and in measurement time is $$\pm\ 1\%$$ then relative error in $$g$$ is: 
  • $$\pm 0.04$$
  • $$0.00$$
  • $$\pm 0.03$$
  • $$\pm 0.01$$
Suppose an attractive nuclear force acts between two protons, which may be written as $$F=\dfrac { { Ae }^{ -kr } }{ { r }^{ 2 } } $$. The dimensional formula for $$\dfrac {A}{K}$$ is 
  • $${M}^{1}{L}^{2}{T}^{2}$$
  • $${M}^{1}{L}^{3}{T}^{-1}$$
  • $${M}^{1}{L}^{4}{T}^{1}$$
  • $${M}^{1}{L}^{4}{T}^{-2}$$
The dimensions of magnetic flux are?
  • $$\left[ ML{ T }^{ -2 }{ A }^{ -2 } \right] $$
  • $$\left[ M{ L }^{ 2 }{ T }^{ -2 }{ A }^{ -2 } \right] $$
  • $$\left[ M{ L }^{ 2 }{ T }^{ -1 }{ A }^{ -2 } \right] $$
  • $$\left[ M{ L }^{ 2 }{ T }^{ -2 }{ A }^{ -1 } \right] $$
Find the dimension of $$\dfrac {G}{4\pi \epsilon_{0}}$$, where $$G$$ is universal gravitation constant and $$\epsilon_{0}$$ is permittivity
of free space.
  • $$[M^{-2}A^{2}T^{2}]$$
  • $$[M^{-2}L^{4}T^{4}A^{-2}]$$
  • $$[M^{0}L^{6}T^{-6}A^{-2}]$$
  • $$[M^{2}A^{2}T^{2}]$$
A man of mass $$m$$ is suspended in air by holding the rope of a balloon of mass $$M$$. As the man climbs up the rope, the balloon.
1143397_26ae687435094f5682984be8bba7be58.PNG
  • Moves upward
  • Moves downward
  • Remain stationary
  • Cannot say
If mass (M), velocity (V) and time (T) are taken as fundamental units, then the dimensions of force (F) are 
  • $$[MVT]$$
  • $$[MVT^{-1}]$$
  • $$[M^2VT]$$
  • $$[M^{-1}V^{-1}T]$$
Order of $$\frac { 1 } { 8 \times 10 ^ { 9 } }$$ is:
  • $$1.77\times {{10}^{-10}}$$
  • $$1.25\times {{10}^{-10}}$$
  • $$1.55\times {{10}^{-10}}$$
  • $$1.95\times {{10}^{-10}}$$
The time of 25 oscillations of a simple pendulum is measured to be $$50.0 s$$ by a watch of least count $$0.1 s$$. The percentage error in time is
  • $$0.2 \%$$
  • $$0.02 \%$$
  • $$0.002 \%$$
  • $$2 \%$$
'The parallax angle in radians is: $$\theta = \left( 1 + \frac { 54 } { 60 } \right) \times \frac { \pi } { 180 } = 0.03316 \mathrm { rad }$$
  Hence, the distance between moon and earth: 
  • $$\dfrac { \text { Diameter of Earth } } { \theta }$$
  • $$\dfrac { 1.276 \times 10 ^ { 7 } m } { 0.03316 }$$
  • $$3.84 \times 10 ^ { 8 } m$$
  • nnone of these
If C is the capacity and V is the potential across the condenser, what will be the dimensional representation of  $$\dfrac1 2 C V ^ { 2 }$$?
  • $$M L ^ { 2 } T ^ { -2 } A ^ { 2 }$$
  • $$\mathrm { ML } ^ { - 2 } \mathrm { T } ^ { - 2 }$$
  • $$M L ^ { 2 } T ^ { - 3 } A ^ { - 2 }$$
  • $$\mathrm { ML } ^ { 2 } \mathrm { T } ^ { - 2 }$$
The length of a rod is (11.05 $$\pm$$ 0.2) cm. What is the length of the two rods?
  • (22.1 $$\pm$$ 0.05) cm
  • (22.1 $$\pm$$ 0.1) cm
  • (22.10 $$\pm$$ 0.05) cm
  • (22.10 $$\pm$$ 0.4) cm
The period of osciflation of a simple pendulum in the recorded as $$2.63 \,sec, 2.42 \,sec, 2.42 \,sec, 2.71 \,sec$$ and $$2.80 \,sec$$ respectively. The average absolute error is
  • $$0.1 \,sec$$
  • $$0.14 \,sec$$
  • $$0.01 \,sec$$
  • $$1.0 \,sec$$
$$X = 3YZ^{2}$$ find dimension of $$Y$$ in $$(MKSA)$$ system, if $$X$$ and $$Z$$ are the dimension of capacity and magnetic field respectively.
  • $$M^{-3}L^{-2}T^{-4}A^{-1}$$
  • $$ML^{-2}$$
  • $$M^{-3}L^{-2}T^{4}A^{4}$$
  • $$M^{-3}L^{-2}T^{8}A^{4}$$
The quantity $$X$$ is given by $${\varepsilon _o}L\frac{{\Delta V}}{{\Delta T}}$$, where $${\varepsilon _o}$$ is the permittivity of free space, $$L$$ is a length, $${\Delta V}$$ is a potential difference and $${\Delta T}$$ is a time interval. The dimensional formula for $$X$$ is the same as that of 
  • resistance
  • charge
  • voltage
  • current
The accuracy in the measurement of the diametre of a hydrogen atom as $${ 1.06\times 10 }^{ -10 }$$ m is
  • $$0.01$$
  • $${ 106\times 10 }^{ -10 }$$
  • $$\dfrac { 1 }{ 106 } $$
  • $${ 0.01\times 10 }^{ -10 }$$
The physical quantity having the dimensions $$[{ M }^{ -1 }{ L }^{ -3 }{ T }^{ 3 }{ A }^{ 2 }]$$ is
  • resistance
  • resistivity
  • electric cunductivity
  • electromotive force
The diameter of wire measured with a varnier calliper with keast count 0.1 mm is Scm, then the percentage error in measurement is
  • $$0.2\%$$
  • $$2\%$$
  • $$5\%$$
  • $$0.5\%$$
A boy wants to buy new shoes. To find out his correct shoe size the ________ of his feet should be measured.
  • Length
  • Thickness
  • Area
  • Volume
If error in measurement of radius of a sphere is $$1\%$$, what will be the error in measurement volume?
  • $$1\%$$
  • $$\dfrac{1}{3}\%$$
  • $$3\%$$
  • None of these
Which of the following measurements is most accurate?
  • $$0.005 mm$$
  • $$5.00 mm$$
  • $$50.00 mm$$
  • $$5.0 mm$$
The dimensions of latent heat are - 
  • $$M ^ { 0 } L ^ { 2 } T ^ { - 2 }$$
  • $$M ^ { 0 } L ^ { 1 } T ^ { - 2 }$$
  • $$M ^ { 2 } L ^ { 0 } T ^ { - 2 }$$
  • $$M ^ { 0 } L ^ { - 2 } T ^ { - 2 }$$
The dimensions of electric potential are:
  • $$\left[ {M{L^2}{T^{ - 2}}{Q^{ - 1}}} \right]$$
  • $$\left[ {ML{T^{ - 2}}{Q^{ - 1}}} \right]$$
  • $$\left[ {M{L^2}{T^{ - 1}}Q} \right]$$
  • $$\left[ {M{L^2}{T^{ - 2}}Q} \right]$$
The dimensions of elelctrical permittivity are
  • $$\left[ {{A^{ - 2}}{M^0}{L^{ - 3}}{T^4}} \right]$$
  • $$\left[ {{A^2}{M^{ - 1}}{L^{ - 3}}{T^0}} \right]$$
  • $$\left[ {A{M^{ - 1}}{L^{ - 3}}{T^4}} \right]$$
  • $$\left[ {{M^{ - 1}}{L^{ - 3}}{T^4}}{A^2} \right]$$
If pressure $$P$$, area $$A$$ and length $$L$$ are taken to be fundamental quantities in a system of units, then energy has dimensional formula.
  • $$P^{1}A^{1}L^{1}$$
  • $$P^{1}A^{3/2}L^{0}$$
  • $$P^{1}A^{0}L^{3}$$
  • Cannot take $$P, A$$ and $$L$$ as fundamental quantities
The error in the measurement of length of a simple pendulum is $$0.1\%$$ and error in the time period is $$2 \%$$. The possible maximum error in the quantity having dimensional formula $$LT^{-2}$$ is
  • $$1.1 \%$$
  • $$2.2\%$$
  • $$4.1\%$$
  • $$6.1\%$$
Of the following quantities , which one has dimensions different from the remaining three?
  • Energy per unit volume
  • Force per unit area
  • Product of voltage and charge per unit volume
  • Angular momentum
The dimensional formula of $$ \frac{GM_{e}}{gRe^{2}}$$ is ---------
  • $$M^{1}L^{1}T^{2} $$
  • $$M^{1}L^{-1}T^{1} $$
  • $$M^{2}L^{-1}T^{2} $$
  • $$M^{0}L^{1}T^{0} $$
If $$m,e,{\varepsilon _0},$$ and $$c$$ denote mass electron, charge of electron Plank's constant and speed of light, respectively. The dimensions of $$\frac{{m{e^4}}}{{\varepsilon _0^2{h^3}c}}$$ are 
  • $$\left[ {{M^0}{L^0}{T^{ - 1}}} \right]$$
  • $$\left[ {{M^0}{L^{ - 1}}{T^{ - 1}}} \right]$$
  • $$\left[ {{M^0}L{T^{ - 3}}} \right]$$
  • $$\left[ {{M^2}{L^{ - 1}}{T^0}} \right]$$
Which of the following pair does not have identical dimension ?
  • Moment of inertia and moment of force
  • Angular momentum and plank's constant
  • Impulse and momentum
  • Work and torque.
The dimensions of $$\cfrac{1}{2}{\in }_{0}{E}^{2}$$, where $${\in }_{0}$$ is permittivity of free space and $$E$$ is electric field, is:
  • $$\left[ M{ L }^{ }{ T }^{ -1 } \right] $$
  • $$\left[ M{ L }^{ 2 }{ T }^{ -2 } \right] $$
  • $$\left[ M{ L }^{ -1 }{ T }^{ -2 } \right] $$
  • $$\left[ M{ L }^{ 2 }{ T }^{ -1 } \right] $$
Out of the following the more precise value is .....
  • $$1.200 \times 10 ^ { 3 } k m$$
  • $$1.20 \times 10 ^ { 3 } k m$$
  • $$1.2 \times 10 ^ { 3 } k m$$
  • $$1200 k m$$
A uniform rod undergoes a longitudinal strain of $$2$$. find percentage change in its volume if poisson's ratio of the material is $$0.50$$
  • 0.4%
  • 0.7%
  • 0%
  • 0.3%
Which of the following pairs of physical quantities have same dimension$$?$$
  • force and work
  • torque and energy
  • torque and power
  • force and torque
An equation is given by $$\dfrac{d}{dt}[\int\vec{v}.\vec{dS}]$$-$$k[\vec{v}.\vec{\theta}]$$. If $$\vec{v}$$ represents velocity, $$\vec{ds}$$ is small dosplacement, $$t$$ is time and a is acceleratation. The dimension of $$k$$ is 
  • $$[T]$$
  • $$[T^{-1}]$$
  • $$[T^{-2}]$$
  • $$[L]$$
The dimensions of $$\frac{1}{{{\mu _0}{ \in _0}}}$$ is (where symbols have their usual menaing)
  • $$\left[ {{L^2}{T^{ - 2}}} \right]$$
  • $$[A]$$
  • $$[ML^2T^{-2}]$$
  • $$[ML^{-2}T^{-2}$$
$$\left[M^{1}L^{2}T^{-3}\right]$$ are the dimensions  of ....
  • pressure
  • power
  • force
  • work
If % error in length, diameter, current and voltage are same than which of the following affects % error in measurement of resistivity, the most:
  • length measurement
  • voltage measurement
  • current measurement
  • diameter measurement
The resultant of two equal forces acting at right angles to each other is $$1414$$ dyne. Find the magnitude of either force.
  • $$960$$
  • $$1000$$
  • $$1200$$
  • $$1414$$
The sum of the numbers $$436.32$$, $$227.244$$ and $$0.301$$ in appropriate significant figures is:
  • $$663.821$$
  • $$664$$
  • $$663.8$$
  • $$663.82$$
The dimensional formula for plank's constant and angular momentum are
  • $$\left[ M{ L }^{ 2 }{ T }^{ -2 } \right] and \left[ ML{ T }^{ -1 } \right] $$
  • $$\left[ M{ L }^{ 2 }{ T }^{ -1 } \right] and \left[ ML^{ 2 }{ T }^{ -1 } \right] $$
  • $$\left[ M{ L }^{ 3 }{ T }^{ 1 } \right] and \left[ ML^{ 2 }{ T }^{ -2 } \right] $$
  • $$\left[ M{ L }^{ 2 }{ T }^{ -1 } \right] and \left[ ML^{ 2 }{ T }^{ -2 } \right] $$
The velocity of a particle varies with distance x from a fixed origin as $$v=Ax+\dfrac { { Bx }^{ 2 } }{ C+x } $$, where A,B and C are dimensional constant then the dimensional formula of $$\dfrac { AB }{ C } $$ is 
  • $$\left[ ML{ T }^{ -2 } \right] $$
  • $$\left[ M^{ 0 }L^{ -1 }{ T }^{ -2 } \right] $$
  • $$\left[ ML^{ -1 }{ T }^{ -2 } \right] $$
  • $$\left[ M^{ 0 }L^{ 0 }{ T }^{ -2 } \right] $$
Given $$m$$ is the mass per unit length, $$T$$ is the tension $$\& L$$ is the length of the wire the dimensional formula for $$L \left( \cfrac { m } { T } \right) ^ { 1 / 2 }$$ is same as that for:- 
  • Wavelength
  • velocity
  • Time period
  • Frequency
The physical quantity having the dimensions$$\left[ { M }^{ -1 }{ L }^{ -3 }{ T }^{ 3 }{ A }^{ 2 } \right] $$ IS
  • resistance
  • resistivity
  • electrical conductivity
  • electromotive force
Dimensions of electrical resistance are :
  • $$[ML^2T^{-3}A^{-1}]$$
  • $$[ML^2T^{-3}A^{-2}]$$
  • $$[ML^3T^{-3}A^{-2}]$$
  • $$[ML^2T^{3}A^{2}]$$
The dimension of $$ (\mu _{ 0 }\epsilon _{ 0 })^{-1/2} $$ are:
  • $$ [L^{1/2}T^{1/2}] $$
  • $$ [L^{1/2}T^{-1/2}] $$
  • $$ [L^{-1}T] $$
  • $$ [LT^{-1}] $$
The electric field in a certain region is given by $$ \overrightarrow E=( \frac {K}{x^3}) \hat i $$. the dimension of K are:-
  • $$ MLT^{-3}A^{-1} $$
  • $$ ML^{-2}T^{-3}A^{-1} $$
  • $$ ML^4T^{-3}A^{-1} $$
  • $$ M^0L^0T^0A^0 $$
A thermometer reads 0$$^{o}$$C as 10 $$^{o}$$C and 100$$^{o}$$C as 90$$^{o}$$C then 
Find the correct temperature if the thermometer reads 20$$^{o}$$C
  • $$20^{o}$$C
  • $$12.5^{o}$$C
  • $$25^{o}$$C
  • $$30^{o}$$C
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