CBSE Questions for Class 11 Engineering Physics Units And Measurement Quiz 13 - MCQExams.com

The dimension of $$ \cfrac {1}{2}\epsilon_o E^2$$ permittivity of free space and E:
Intensity of electric field) is



      
  • $$[MLT^{-1}]$$
  • $$[ML^2T^{-1}]$$
  • $$[ML^{-1}T^{-2}]$$
  • $$[ML^2T^{-2}]$$
The radius of a sphere is measured as $$(10 \pm 0.02\ \% )$$ cm. The error in the measurement of its volume is 
  • $$25.1$$ cc
  • $$25.12$$ cc
  • $$2.51$$ cc
  • $$251.2$$ cc
A particle is moving with a velocity $$35\ m/s$$ along positive x-axis.It's acceleration is towards negative X-axis with the magnitude $$4m/s^ {2}$$ then the distance covered by the particle in the $$9th$$ second:-
  • $$1m$$
  • $$\dfrac {9}{8}m$$
  • $$\dfrac {5}{4}m$$
  • $$153m$$
The vector sum of three forces having magnitudes $$ | \overrightarrow F_1 | = 100 N $$,  $$ | \overrightarrow F_2 | = 80 N $$ &  $$ | \overrightarrow F_3 | = 60 N $$ acting on a particle is zero. the angle between $$ \overrightarrow F_1$$  & $$ \overrightarrow F_2 $$ is nearly:-
  • $$ 53^0 $$
  • $$ 143^0 $$
  • $$ 37^0 $$
  • $$ 127^0 $$
Two constant force $$ \overrightarrow F_1 and \overrightarrow F_2 $$ acts on a body.these forces displaces the body from point P(1, -2, 3) to Q (2, 3, 7 ) in 2s starting from rest.force $$\overrightarrow F_1 $$ is of magnitude 9 N and acting along vector $$ ( 2 \hat i - 2 \hat j + \hat k ) $$ . the positions are in meter. find work done by $$ \overrightarrow F_1 $$.
  • $$-12J$$
  • $$+12J$$
  • $$36J$$
  • $$-36J$$
A force is given by $$F = at + b{t^2}$$, where $$t$$ is time, the dimensions of $$a$$ and $$b$$ are respectively :
  • $$\left[ {ML{T^{ - 4}}} \right]$$ and $$\left[ {ML{T^{ - 1}}} \right]$$
  • $$\left[ {ML{T^{ - 1}}} \right]$$ and $$\left[ {ML{T^0}} \right]$$
  • $$\left[ {ML{T^{ - 3}}} \right]$$ and $$\left[ {ML{T^{ - 4}}} \right]$$
  • $$\left[ {ML{T^{ - 3}}} \right]$$ and $$\left[ {ML{T^0}} \right]$$
The radius of a sphere is measured to be $$(4.0 +2.0)$$ cm the maximum percentage error in the measurement of the volume of the sphere is 
  • $$10$$ %
  • $$15$$ %
  • $$20 $$%
  • $$25$$ %
If the constant of gravitation $$(G)$$, Planck's constant $$(h)$$ and the velocity of light $$(c)$$ be chosen as fundamental units. The dimension of the radius of gyration is
  • $$h^{-1/2} c^{1/2} G^{1/2}$$
  • $$h^{1/2} c^{-3/2} G^{1/2}$$
  • $$h^{1/2} c^{-3/2} G^{-1/2}$$
  • $$h^{-1/2} c^{-3/2} G^{1/2}$$
In the equation $${ S }_{ nth }=u+\dfrac { a }{ 2 } \left( 2n-1 \right) $$, the letters have their usual meanings. The dimensional formula of $$S_{nth}$$ is
  • $$\left[ { ML }^{ 0 }T \right] $$
  • $$\left[ { ML }^{ -1 }T^{ -1 } \right] $$
  • $$\left[ { M^{ 0 }L }T^{ -1 } \right] $$
  • $$\left[ { M^{ 0 }L }T^{ 0 } \right] $$
A physical quantity x depends on quantities y and Z as follows  : x= Ay+B tan (Cz), where A, B and C are constants . Which of the following do not have same dimensions ?
  • x and B
  • C and $$z^{ -1 }$$
  • y and B/A
  • x and A
The term $$(1/2)pv^{ 2 }$$ occurs in Bernoulli's  equation , with $$\beta $$ being the density of fluid and V its speed . The dimensions of this term are 
  • $$\left[ { M }^{ -1 }{ L }^{ 5 }{ T }^{ 2 } \right] $$
  • $$\left[ { M }{ L }{ T }^{ 2 } \right] $$
  • $$\left[ { M }{ L }^{ -1 }{ T }^{ -2 } \right] $$
  • $$\left[ { M }^{ -1 }{ L }^{ 9 }{ T }^{ -2 } \right] $$
Two resistance are measured in ohm and is given as:-
$${ R }_{ 1 }=3\Omega \neq 1%$$
$${ R }_{ 2 }=6\Omega \neq 2%$$
When they are connectrd in parallel, the percentage error in equivalent resistance is
  • $$3.33\%$$
  • $$4.5\%$$
  • $$0.67\%$$
  • $$1.33\%$$
The pair of physical quantities, that have difference dimensions is 
  • Planck's constant and angular momentum
  • Energy density and pressure
  • Relative density and plane angle
  • Specific heat capacity and latent heat
The dimension of the ratio of magnetic flux and the resistance is equal to that of:
  • induced emf
  • charge
  • inductance
  • current
If pressure is (P), velocity (V), and time (T) are taken as the fundamental quantities, then the dimensional formula of force is
  • $$\left[ P ^ { 1 } V ^ { 1 } T ^ { 1 } \right]$$
  • $$\left[ P ^ { 1 } V ^ { 2 } T ^ { 1 } \right]$$
  • $$\left\lceil P ^ { 1 } V ^ { 1 } T ^ { 2 } \right\rceil$$
  • $$\left[ P ^ { 1 } V ^ { 2 } T ^ { 2 } \right]$$
In a system of units if force (F), acceleration (A) and time, (T) are taken as fundamental units then the dimensional formula of energy is -
  • $$FA^{2}T$$
  • $$FAT^{2}$$
  • $$F^{2}AT$$
  • FAT
If the radius of the earth were to shrink by 1% its mass remaining the same, the acceleration due to gravity on the earth's surface would
  • Decreased by 2%
  • Increased by 2%
  • Remain unchanged
  • Increased by 1%
Dimensional formula $$[{ M }^{ 1 }{ L }^{ 0 }{ T }^{ -2 }]$$ is equal to dimensional formula of 
  • Surface tension
  • surface energy
  • Both A and B
  • None of these
Dimensional formula of momentum is :
  • $$MLT$$
  • $$M^{-1} L^{-1} T^{-1}$$
  • $$ML^{-1} T^{-1}$$
  • $$MLT^{-1}$$
Dimensions of rate of change of flux are equivalent to those of 
  • voltage
  • current
  • 1/charge
  • charge
If  $$S = \dfrac { d } { t } + \dfrac { e } { ( f - t ) ^ { 2 } } ,$$  where  $$S$$  is the displacement of the body in time  $$t .$$  Find the dimensions of  $$e$$  and  $$f$$
  • $$\mathrm { LT } , \mathrm { T }$$
  • $$\mathrm { LT } ^ { 2 } , \mathrm { T }$$
  • $$\mathrm { L } ^ { 2 } \mathrm { T } , \mathrm { T } ^ { - 3 }$$
  • $$LT, T ^ { 2 }$$
The dimensional formula for the acceleration, velocity and length are $$\alpha { \beta  }^{ -2 }, \alpha { \beta  }^{  -1 }$$ and $$\alpha y$$. What is the dimensional formula for the coefficient of friction ? 
  • $$\alpha \beta y$$
  • $${ \alpha }^{  -1 }{ \beta }^{ 10 }{ y }^{ 0 }$$
  • $${ \alpha }^{ 0 }{ \beta }^{ -1 }{ y }^{ 0 }$$
  • $${ \alpha }^{  0 }{ \beta }^{ 0 }{ y }^{ 0 }$$
The dimensions of the ratio of angular momentum to linear momentum:
  • $$\left[ { M }^{ 1 }{ L }^{ -3 }{ T }^{ 0 } \right] $$
  • $$\left[ { M }^{ 0 }{ L }^{ 1 }{ T }^{ -2 } \right] $$
  • $$\left[ { M }^{ 0 }{ L }^{ 0 }{ T }^{ -1 } \right] $$
  • $$\left[ { M }^{ 0 }{ L }^{ 1 }{ T }^{ 0 } \right] $$
The dimensions of universal gas constant is
  • $$\left[ { M }^{ }{ L }^{ 2 }{ T }^{ -2 }{ \theta }^{ -1 } \right] $$
  • $$\left[ { M }^{ 2 }{ L }^{ }{ T }^{ -2 }{ \theta }^{ } \right] $$
  • $$\left[ { M }^{ }{ L }^{ 3}{ T }^{ -1 }{ \theta }^{ -1 } \right] $$
  • None of these
Velocity gradient has same dimensional formula as
  • Frequency
  • angular momentum
  • velocity
  • none of these
The dimension of electric permittivity is
  • $$M{L}^{3}{T}^{4}{A}^{-2}$$
  • $$M{L}^{-3}{T}^{4}{A}^{2}$$
  • $${M}^{-1}{L}^{3}{T}^{4}{A}^{2}$$
  • $${M}^{-1}{L}^{-3}{T}^{4}{A}^{2}$$
Find dimension formula of polarisation?
  • $$\left[ { L }^{ -2 }T^{ 1 }{ A }^{ 1 } \right] $$
  • $$\left[ { L }^{ 2 }T^{ 1 }{ A }^{ -1 } \right] $$
  • $$\left[ { L }^{ 2}T^{ 1 }{ A }^{ 1} \right] $$
  • $$\left[ { L }^{ -3}T^{ -1 }{ A }^{ 1} \right] $$
If $$\eta$$ represents the coefficient of viscosity and $$T$$ the surface tension, then the dimension of $$\cfrac{T}{\eta}$$ is same as that of:
  • length
  • mass
  • time
  • speed
Dimensional formula of modulus of elasticity is
  • $$\left[ M ^ { 0 } L ^ { - 1 } T ^ { - 2 } \right]$$
  • $$\left[ M ^ { 1 } L ^ { - 1 } T ^ { - 2 } \right]$$
  • $$\left[ M ^ { 1 } L ^ { 1 } T ^ { - 2 } \right]$$
  • $$\left[ M ^ { -1 } L ^ { - 1 } T ^ { - 2 } \right]$$
Given  $$x = a + b t + c t ^ { 2 }$$  where  $$x$$  in metre and  $$t$$  in second. Find the dimensional formula of  $$b$$
  • $$L$$
  • $$L T ^ { - 1 }$$
  • $$L T ^ { - 2 }$$
  • $$L ^ { 2 }$$
The radius of nucleus is $$r = r_0 A^{{1}/{3}}$$, where $$A$$ is mass number. The dimensions of $$r_0$$ is 
  • $$[MLT^{-2}]$$
  • $$[M^0 L^0 T^{-1}$$
  • $$[M^0 L T^0]$$
  • None of these
If L be the inductance, R resistance and C be the capacitance of a capacitor, then dimensional formula of $$ \cfrac {L}{R} $$ and RC are
  • $$ M^oLT^{-1}ML ^oT^{-1} $$
  • $$ M^oL^oT,MLT^o $$
  • $$ M^oL^oT, 1 $$
  • $$ M^oL^oT, M^oL^oT $$
The dimensions of $$(\mu_{0}\epsilon_{0})^{-\dfrac {1}{2}}$$ are
  • $$[L^{-\dfrac {1}{2}} T^{\dfrac {1}{2}}]$$
  • $$[L^{\dfrac {1}{2}} T^-{\dfrac {1}{2}}]$$
  • $$[L^{-1} T]$$
  • $$[L T^{-1}]$$
If C be the capacitance and V be the electric potential,then the dimensional formula of $$ CV^2 $$ is 
  • $$ [ML ^{-3} TA] $$
  • $$ [M^oLT^{-2} A^o] $$
  • $$ [ML ^1 A^{-1 }] $$
  • $$ [ML^2T^{-2} A^o] $$
Given  $$x = a + b t + c t ^ { 2 }$$  where  $$x$$  in metre and  $$t$$  in second. Find the dimensional formula of  $$C$$
  • $$L$$
  • $$L T ^ { - 1 }$$
  • $$L T ^ { - 2 }$$
  • $$L ^ { 2 } T ^ { 2 }$$
Given that m is the mass suspended from a spring  force constant k. The dimension of the formula for $$\sqrt{m/k}$$ is same as that for 
  • frequency
  • time period
  • velocity
  • wavelength
Velocity gradient has dimension of
  • Force  
  • Frequency
  • Surface tension 
  • momentum 
The Earth's radius is $$6371\ km$$. The order of magnitude of the Earth's radius is
  • $$10^3$$
  • $$10^2$$
  • $$10^7$$
  • $$10^5$$
The diagram shows a cuboid block made from a metal of density $$2.5g/{cm}^{3}$$
What is the mass of the block?
1647084_f928bdb31fbb4bd0b578f2af7b6d3ebe.png
  • $$8.0kg$$
  • $$16kg$$
  • $$50g$$
  • $$100g$$
The dimensional formula of pressure is 
  • $$ [MLT^{-2} ] $$
  • $$ [ML^2T^{-2} ] $$
  • $$ [ML^{-1}T^{-2} ] $$
  • $$ [M^0L^{-1}T^{-2} ] $$
The dimension of $$ \frac {1}{2} \varepsilon _ o E^2 ( \varepsilon _ o $$  is the permitivity of free space and E is electric field) is 
  • $$ [ML^2T^{-1} ] $$
  • $$ [ML^{-1} T^{2} ] $$
  • $$ [ML^2 T^{-2} ] $$
  • $$ [MLT^{-1} ]$$
In the density measurement of a cube, the mass an edge length are measured as $$\left( 10.00\pm 0.10 \right) kg$$ and $$\left( 0.10\pm 0.01 \right) m$$, respectively. The error in the measurement of density:
  • $$0.10kg/{m}^{3}$$
  • $$0.31kg/{m}^{3}$$
  • $$0.07kg/{m}^{3}$$
  • $$0.01kg/{m}^{3}$$
  • No answer
The dimensional formula for the magnetic fields is 
  • $$ [MT^{-2} A^{-1} ] $$
  • $$ [ML^2T^{-1}A^{-2} ] $$
  • $$ [MT^{-2}A^{-2}] $$
  • $$ [MT^{-1} A^{-2}] $$
The dimension of Magnetic flux.
  • $$ML^{2}I^{-1}T^{-3}$$
  • $$ML^{2}I^{-4}T^{-2}$$
  • $$ML^{2}I^{-1}T^{-2}$$
  • None of these
Which of the following does not have the dimension of force?
  • Potential gradient
  • Energy gradient
  • Weight
  • Rate of change of momentum
If $$P$$ and $$Q$$ have different non-zero dimensions, which of the following operations is possible?
  • $$P+Q$$
  • $$PQ$$
  • $$P-Q$$
  • $$ 1-\dfrac{P}{Q} $$
The pairs of physical quantities that have the same dimensions in (are):
  • Reynolds number and coefficient of friction
  • Curie and frequency of a light wave
  • Latent heat and gravitational potential
  • Planck's constant and torque
Taking frequency $$f$$, velocity $$v$$ and density $$\rho$$ to be the fundamental quantities then the dimensional formula for momentum will be?
  • $$\rho v^4f^{-3}$$
  • $$\rho v^3f^{-1}$$
  • $$\rho v f^2$$
  • $$\rho^2v^2f^2$$
If  x,v and a denote the displacement, the velocity and the acceleration of a particle
executing simple harmonic motion of time period T, then which of the following do not
change with time?
  • $$\dfrac{aT}{v}$$
  • $$aT+2\pi v$$
  • $$a^2T^2+4\pi^2 v^2$$
  • $$aT$$
  • $$vT$$
The dimensions of time constant are:
  • $$[M^0L^0T^0]$$
  • $$[M^0L^0T]$$
  • $$[MLT]$$
  • None of these
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