CBSE Questions for Class 11 Engineering Physics Units And Measurement Quiz 14 - MCQExams.com

The equation of alternating current $$I=I_0e^{-t/CR}$$, where $$t$$ is time, $$C$$ is capacitance and $$R$$ is resistance of coil, then the dimensions of $$CR$$ is?
  • $$[MLT^{-1}]$$
  • $$[M^0LT]$$
  • $$[M^0L^0T]$$
  • None of these
In the equation $$y=a\sin(\omega t+kx)$$, the dimensional formula of $$\omega$$ is?
  • $$[M^0L^0T^{-1}]$$
  • $$[M^0LT^{-1}]$$
  • $$[ML^0T^0]$$
  • $$[M^0L^{-1}T^0]$$
The mass of a neutral carbon atom in ground state is 
  • exact $$12\,u$$
  • less than $$12\,u$$
  • more than $$12\,u$$
  • depends on the form of carbon such as graphite a=or charcoal
Which of the following statement is correct about conversion of units, for example $$1 m = 100 cm$$
  • Conversion of units have identical dimensions on each side of the equal sign but not the same units.
  • Conversion of units have identical dimensions on each side of the equal sign but the same units.
  • If a larger unit is used then numerical value of physical quantity is large
  • Due to conversion of units physical quantity to be measured will change.
Which of the following sets have different dimensions?
  • Pressure, Young's modulus, stress
  • Emf, potential difference, electric potential
  • Heat, work done, energy
  • Dipole moment, electric flux, electric field
Out of the following the only pair that does not have identical dimensions is 
  • angular momentum and Planck's constant
  • moment of inertia and moment of a force
  • work and torque
  • impulse and momentum
The physical quantities not having same dimensions are 
  • torque and work
  • momentum and Planck's constant
  • stress and young's modulus
  • speed and $$ \left ( \mu_{0}\varepsilon _{0} \right )^{-1/2} $$
If the momentum (P), area (A) and time (T) are taken to be fundamental quantities, then energy has dimensional formula.
  • $$\left [P^{1} A^{-1} T^{1} \right ]$$
  • $$\left [P^{2} A^{-1} T^{1} \right ]$$
  • $$\left [P^{1} A^{-1/2} T^{1} \right ]$$
  • $$\left [P^{1} A^{1/2} T^{-1} \right ]$$
The dimensional representation of $$ab/RT$$ is 
  • $$ML^5 T^{-2}$$
  • $$M^0 L^3 T^0$$
  • $$ML^{-1} T^{-2}$$
  • None of these
Mass varies from place to place but weight does not .
  • True
  • False
State if the following statements are true or false. Correct the statement if it is false.
The length of an irregular object can be found with the help of a graph paper.
  • True
  • False
Weight always acts vertically downwards.
  • True
  • False
State if the following statements are true or false. Correct the statement if is is false.
$$1 \,m = 10,000 \,cm^3$$
  • True
  • False
(d) The correct relation is:
  • d= $$ M\times V $$
  • M= $$ d\times V $$
  • V= $$ d\times M $$
  • d= $$M+V$$

The image formed by a plane mirror can be obtained on a screen.
  • True
  • False
The earth attracts a body of mass $$1$$ kg with a force of $$10$$ N. The mass of boy is $$50$$ kg. His weight will be
  • $$50$$ kg
  • $$500$$ N
  • $$50$$ N
  • $$5$$ N
The magnitude of any physical quantity
  • Depends on the method of measurement
  • Does not depend on the method of measurement
  • Is more in SI system than in CGS system
  • Directly proportional to the fundamental units of mass, length
    and time
The angle of incidence on the plane mirror is The angle between the incident ray and the reflected ray is:
  • 30
  • 15
  • 60
  • 90
The dimension of quantity (L / RCV) is
  • $$[A]$$
  • $$[A^2]$$
  • $$[A^{-1}]$$
  • None of these
Which pair has the same dimensions
  • Work and power
  • Density and relative density
  • Momentum and impulse
  • Stress and strain
The dimensional formula for impulse is same as the dimensional
formula for
  • Momentum
  • Force
  • Rate of change of momentum
  • Torque
The dimensions of "time constant" $$\dfrac{L}{R}$$ during growth and decay of current in all inductive circuit is same as that of
  • Constant
  • Resistance
  • Current
  • Time
In the following list, the only pair which have different dimensions,is
  • Linear momentum and moment of a force
  • Planck's constant and angular momentum
  • Pressure and modulus of elasticity
  • Torque and potential energy
The pair having the same dimensions is
  • Angular momentum, work
  • Work, torque
  • Potential energy, linear momentum
  • Kinetic energy, velocity
The dimensions of surface tension are
  • $$ML^{-1}T^{-2}$$
  • $$MLT^{-2}$$
  • $$ML^{-1}T^{-1}$$
  • $$MT^{-2}$$
The dimensions of $$CV^2$$ matches with the dimensions of
  • $$L^2 I$$
  • $$L^2 I^2$$
  • $$L I^2$$
  • $$\dfrac{1}{LI}$$
The dimensional formula for r.m.s. (root mean square) velocity is
  • $$M^0LT^{-1}$$
  • $$M^0L^0T^{-2}$$
  • $$M^0L^0T^{-1}$$
  • $$MLT^{-3}$$
If C and L denote capacitance and inductance respectively, then the dimensions of LC are
  • $$M^0L^0T^0$$
  • $$M^0L^0T^2$$
  • $$M^2L^0T^2$$
  • $$MLT^2$$
Dimensions of CR are those of
  • Frequency
  • Energy
  • Time period
  • Current
The dimensional formula for young's modulus is
  • $$ML^{-1}T^{-2}$$
  • $$M^0LT^{-2}$$
  • $$MLT^{-2}$$
  • $$ML^{2}T^{-2}$$
Which of the following quantities is dimensionless
  • Gravitational constant
  • Planck's constant
  • Power of a convex lens
  • None
The dimensions of pressure is equal to
  • Force per unit volume
  • Energy per unit volume
  • Force
  • Energy
The dimension of $$\dfrac{R}{L}$$ are
  • $$T^2$$
  • $$T$$
  • $$T^{-1}$$
  • $$T^{-2}$$
The dimensions of inter atomic force constant are
  • $$MT^{-2}$$
  • $$MLT^{-1}$$
  • $$MLT^{-2}$$
  • $$ML^{-1}T^{-1}$$
Which physical quantities have the same dimension  
  • Couple of force and work
  • Force and power
  • Latent heat and specific heat
  • Work and power
Pressure gradient has the same dimension as that of
  • Velocity gradient
  • Potential gradient
  • Energy gradient
  • None of these
If R and L represent respectively resistance and self inductance,which of the following combinations has the dimensions of frequency
  • $$\dfrac{R}{L}$$
  • $$\dfrac{L}{R}$$
  • $$\sqrt{\dfrac{R}{L}}$$
  • $$\sqrt{\dfrac{l}{R}}$$
The dimensions of shear modulus are
  • $$MLT^{-1}$$
  • $$ML^2T^{-2}$$
  • $$ML^{-1}T^{-2}$$
  • $$MLT^{-2}$$
Accuracy of measurement is determined by
  • Absolute error
  • Percentage error
  • Both
  • None of these
What is the number of significant figures in $$0.310\times10^3$$
  • 2
  • 3
  • 4
  • 6
If current in an electric bulb change by $$1$$%, then the power will change by
  • $$1$$%
  • $$2$$%
  • $$4$$%
  • $$\dfrac{1}{2}$$%
Which of the following group have different dimension
  • Potential difference, EMF, voltage
  • Pressure, stress, young's modulus
  • Heat, energy, work-done
  • Dipole moment, electric flux, electric field
The dimensions of magnetic field intensity in $$ M, L , T $$ and $$ C $$ is given as 
  • $$ MT^2 C^{-1} $$
  • $$ MLT^{-1}C^{-1} $$
  • $$ MT^2C^{-2} $$
  • $$ MT^{-1}C^{-1} $$
Which of the following is the best estimate for the mass of all the people living on the Earth?
  • $$2*10^{8}kg$$
  • $$1*10^{9}kg$$
  • $$2*10^{10}kg$$
  • $$3*10^{11}kg$$
  • $$4*10^{12}kg$$
Let $$[\varepsilon _{0}]$$ denote the dimensional formula of the permittivity of vacuum. If $$M=$$ mass, $$L=$$ length, $$T=$$ time and $$A=$$ electric current, then:
  • $$[\varepsilon _{0}]=[M^{-1}L^{-3}T^{4}A^{2}]$$
  • $$[\varepsilon _{0}]=[M^{-1}L^{2}T^{-1}A^{-2}]$$
  • $$[\varepsilon _{0}]=[M^{-1}L^{2}T^{-1}A]$$
  • $$[\varepsilon _{0}]=[M^{-1}L^{-3}T^{2}A]$$
An unknown quantity $$\displaystyle "\alpha"$$ is expressed $$\displaystyle \alpha =\frac{2ma}{\beta }\log \left ( 1+\frac{2\beta \varphi }{ma} \right )$$
where $$m$$ = mass, $$a$$ = acceleration, $$\displaystyle \varphi $$  = length 
The unit of $$\displaystyle \alpha  $$ should be 
  • meter
  • $$m/s$$
  • $$m/s$$$$\displaystyle ^{2}$$
  • $$s$$$$\displaystyle ^{-1}$$
The Bernoulli's equation is given by $$\displaystyle p + \frac {1} {2} \rho v^2 + h \rho g = k $$, 
where $$p$$ = pressure, $$ \rho $$ = density, $$v$$ = speed, $$h$$= height of  the liquid column,$$g$$ = acceleration due to gravity and $$k$$ is constant. The dimensional formula for $$k$$ is same as that for : 
  • Velocity gradient
  • Pressure gradient
  • Modulus of elasticity
  • Thrust
In the relation, $$\displaystyle P=\frac{\alpha }{\beta }e^{{\alpha z}/{k\theta }}$$ $$P$$ is pressure, $$Z$$ is distance, $$K$$ is Boltzmann constant and $$\displaystyle \theta $$ is the temperature. The dimensions of $$\displaystyle \beta $$ will be 
  • $$\displaystyle \left [ M^{\circ}L^{2}T^{0} \right ]$$
  • $$\displaystyle \left [ ML^{2}T \right ]$$
  • $$\displaystyle \left [ ML^{\circ}T^{~1} \right ]$$
  • $$\displaystyle \left [ M^{\circ}L^{2}T^{-1} \right ]$$
If $$E, M, J$$ and $$G$$ respectively denote energy, mass, angular momentum and universal gravitational constant, the quantity, which has the same dimensions as the dimensions of $$\frac{EJ^2}{M^5G^2}$$ is:
  • time
  • angle
  • mass
  • length
Match the following physical quantities with their respective dimensional formula:

(a) Angular Momentum(e) $$\displaystyle \left[ { ML }^{ 2 }{ T }^{ -3 } \right] $$
(b) Impulse(f) $$\displaystyle \left[ { ML }^{ 2 }{ T }^{ -1 } \right] $$
(c) Pressure(g) $$\displaystyle \left[ ML{ T }^{ -1 } \right] $$
(d) Power(h) $$\displaystyle \left[ { ML }^{ -1 }{ T }^{ -2 } \right] $$
  • a-f, b-g, c-h, d-e
  • a-f, b-g, c-e, d-h
  • a-g, b-h, c-f, d-e
  • a-g, b-h, c-e, d-f
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