CBSE Questions for Class 11 Engineering Physics Units And Measurement Quiz 10 - MCQExams.com

While measuring the length of a wooden box, the reading at one end is 1.5 cm and the other end is 4.7 cm. What is the length of the wooden box?
  • 4.7 cm
  • 1.5 cm
  • 3.2 cm
  • 6.2 cm
The position x of a particle at time t is given by $$x = \dfrac{v_{0}}{a}(1 - e^{-at})$$ where $$v_{0}$$ is a constant and a >The dimensional formula of $$v_{0}$$ and a are
  • $$[M^{0}L^{1}T^{-1}] and [M^{0}L^{0}T^{-1}]$$
  • $$[M^{0}L^{1}T^{0}] and [M^{0}L^{0}T^{-1}]$$
  • $$[M^{0}LT^{-1}] and [M^{0}L^{1}T^{-2}]$$
  • $$[M^{0}L^{1}T^{-1}] and [M^{0}L^{0}T^{1}]$$
The dimensional formula for permittivity of free space $$(\epsilon_{0})$$ in the equation $$F = \dfrac {1}{4\pi \epsilon_{0}} \dfrac {q_{1}q_{2}}{r^{2}}$$ where, symbols have their usual meaning is
  • $$[M^{1}L^{3}A^{-2}T^{-4}]$$
  • $$[M^{-1}L^{-3}T^{4}A^{2}]$$
  • $$[M^{-1}L^{-3}A^{-2}T^{-4}]$$
  • $$[M^{1}L^{3}A^{2}T^{-4}]$$
Four pieces of wooden sticks P, Q, R and S are placed along the length of 15 cm long scale as shown in figure. What is the average length of these sticks?
809515_ff76bafc944c4995a06d0c1f9cf23938.png
  • 2.0 cm
  • 2.5 cm
  • 2.6 cm
  • 2.9 cm
If $${ \varepsilon  }_{ 0 }$$ is the permittivity of free space and $$E$$ is the electric field, then the dimensions of $$\cfrac { 1 }{ 2 } { \varepsilon  }_{ 0 }{ E }^{ 2 }\quad $$ is
  • $$\left[ M{ L }^{ }{ T }^{ } \right] $$
  • $$\left[ M{ L }^{ 2 }{ T }^{ -2 } \right] $$
  • $$\left[ M{ L }^{ -1 }{ T }^{ -2 } \right] $$
  • $$\left[ M{ L }^{ 2 }{ T }^{ -1 } \right] $$
For a circuit, L, C and R represent the inductance, capacitance and resistance. Then, the dimensional formula for $$C^2LR$$ is
  • $$[MLT]$$
  • $$[M^0L^0TI^0]$$
  • $$[M^2L^2T^0I^0]$$
  • $$[M^0L^0T^3I^0]$$
$$R,L$$ and $$C$$ represent the physical quantities resistance, inductance and capacitance respectively. Which one of the following combination has dimensions of frequency?
  • $$\cfrac { 1 }{ \sqrt { RC } } $$
  • $$\cfrac { R }{ L } $$
  • $$\cfrac { 1 }{ LC } $$
  • $$\cfrac { C }{ L } $$
The dimensions of angular momentum/ magnetic moment are
  • $$[MA^{-1}T^{-1}]$$
  • $$[M^{-1}AT^{-1}]$$
  • $$[MAT^{-1}]$$
  • $$[MA^{-1}T]$$
The mass of a box measured by a grocer's balance is 2.3 kg. Two gold pieces of masses 20.15 g and 20.17 g are added to the box. The total mass of the box is:
  • 2.3 kg
  • 2.34 kg
  • 2.340 kg
  • 2.3403 kg
A cube has a side of length 1.2 x $$10^{-2}$$. Its volume upto correct significant figures is
  • 1.7 x $$10^{-6}m^3$$
  • 1.73 x $$10^{-6}m^3$$
  • 1.78 x $$10^{-6}m^3$$
  • 1.732 x $$10^{-6}m^3$$
The radius of a sphere is 1.41 cm. Its volume to an appropriate number of significant figures is then
  • 11.73 $$cm^3$$
  • 11.736 $$cm^3$$
  • 11.7 $$cm^3$$
  • 117 $$cm^3$$
The sun's angular diameter is measured to be 1920". The distance of the sun from the earth is $$1.496 \times 10^{11} m$$. What is the diameter of the sun then?
  • $$1.39 \times 10^9 m$$.
  • $$1.39 \times 10^{10} m$$.
  • $$1.39 \times 10^{11} m$$.
  • $$1.39 \times 10^{12} m$$.
Which of the following pairs of physical quantities have same dimensions?
  • Force and power
  • Torque and energy
  • Torque and power
  • Force and torque
The number of significant figure In the numbers $$4.8000 \times 10^4$$ and $$48000.50 $$ are respectively then
  • $$5$$ and $$6.$$
  • $$5$$ and $$ 7$$.
  • $$2$$ and $$7.$$
  • $$2$$ and $$6$$.
Four charges are placed at the circumference of the dial of a clock as shown in figure. If the clock has only hour hand, then the resultant force on a positive charge $$q_{0}$$ placed at the centre, points in the direction which shows the time as :-
872988_7da74d36c1a04929959914ed71a34dfe.png
  • 1:30
  • 7:30
  • 4:30
  • 10:30
The numbers 3.845 and 3.835 on rounding off to 3 significant figures will give then
  • 3.85 and 3.84
  • 3.84 and 3.83
  • 3.85 and 3.83
  • 3.84 and 3.84
Which one of the following methods is used to measure distance of a planet or a star from the earth?
  • Echo method
  • Parallax method
  • Triangulation method
  • None of these
The dimensional formula of electric potential is
  • $$[ML^2T^{-3}A^{-1}]$$
  • $$[M^{-1}L^2T^{-2}A]$$
  • $$[M^{-1}L^2T^{-2}A^{-1}]$$
  • $$[ML^2T^{-2}A]$$
Which of the following relation is dimensionally incorrect?
  • 1 u = 931.5 MeV
  • 1 u = 931.5 MeV/c$$^2$$
  • 1 u = 1.67 x 10$$^{-27}$$kg
  • None of these
The velocity of a particle (v) at an instant t is given by v =at + bt$$^{2}$$. The dimension of b is the
  • $$[L]$$
  • $$[LT^{-1}]$$
  • $$[LT^{-2}]$$
  • $$[LT^{-3}]$$
The numbers $$2.745$$ and $$2.735$$ on rounding off to $$3$$ significant figures will give:
  • $$2.75$$ and $$2.74$$
  • $$2.74$$ and $$2.73$$
  • $$2.75$$ and $$2.73$$
  • $$2.74$$ and $$2.74$$
If E, m, l and G denote energy, mass, angular momentum and gravitational constant respectively, then the quantity $$\displaystyle (\frac {El^2}{m^5G^2})$$ has the dimensions of then
  • mass
  • length
  • time
  • angle.
Dimensional formula of $$\Delta Q$$, heat supplied to the system is
  • $$[ML^2T^{-2}]$$
  • $$[MLT^{-2}]$$
  • $$[ML^2T^{-1}]$$
  • $$[MLT^1]$$
The dimensions of Planck's constant are the same as that of the
  • linear impulse
  • work
  • linear momentum
  • angular
The dimensional formula of physical quantity is $$[M^aL^bT^c]$$. Then that physical quantity is
  • surface tension if a = 1, b = 1, c = -2
  • force if a = 1, b = 1, c = 2
  • angular frequency if a = 0, b = 0, c = -1
  • spring constant if a = 1, b = -1, c = -2
The displacement of a progressive wave is represented by y = A sin($$\omega$$t - kx) where x is distance and t is time. The dimensions of $$\displaystyle \frac{\omega}{k}$$ are same as those of the
  • velocity
  • wave number
  • wavelength
  • frequency
The mean length of an object is 5 cm. Which of the following measurements is most accurate. ?
  • 4.9 cm
  • 4.805 cm
  • 5.25 cm
  • 5.4 cm
The physical quantity to be measured more accurately in the experimental determination of Young's modulus of a wire is
  • Radius
  • Length
  • Force
  • Extension
The dimensional formula for electric intensity is
  • $$\left[ { M }^{ 1 }{ L }^{ 1 }{ T }^{ 3 }{ A }^{ -1 } \right] $$
  • $$\left[ { M }^{ }{ L }^{ -1 }{ T }^{ 3 }{ A }^{ 1 } \right] $$
  • $$\left[ { M }^{ 1 }{ L }^{ 1 }{ T }^{ -3 }{ A }^{ -1 } \right] $$
  • $$\left[ { M }^{ 1 }{ L }^{ 2 }{ T }^{ 1 }{ A }^{ 1 } \right] $$
Consider two cylindrical rods of identical dimensions, one of rubber and the other of steel. Both the rods are fixed rigidly at one end to the roof. A mass $$M$$ is attached to each of the free ends at the centre of the rods.
  • Both the rods will elongate but there shall be no perceptible change in shape
  • The steel rod will elongate and change shape but the rubber rod will only elongate
  • The steel rod will elongate without any perceptible change in shape, but the rubber rod will elongate and the shape of the bottom edge will change to an ellipse
  • The steel rod will elongate, without any perceptible change in shape, but the rubber rod will elongate with the shape of the bottom edge tapered to a tip at the centre
The dimensional formula of electric flux is:
  • $$\left[ { M }^{ 1 }{ L }^{ 1 }{ T }^{ -2 } \right] $$
  • $$\left[ { M }^{ 1 }{ L }^{ 3 }{ T }^{ -3 }{ A }^{ -1 } \right] $$
  • $$\left[ { M }^{ 2 }{ L }^{ 2 }{ T }^{ -2 }{ A }^{ -2 } \right] $$
  • $$\left[ { M }^{ 1 }{ L }^{ -3 }{ T }^{ 3 }{ A }^{ 1 } \right] $$
If E, M, J and G denote energy, mass, angular momentum and gravitational constant respectively, then $$\frac{EJ^2}{M^5 G^2}$$ has the dimensions of 
  • length
  • mass
  • time
  • angle
With due regard to significant figures, add the following:
a. 953 and 0.324
b. 953 and 0.625
c. 953.0 and 0.324
d. 953.0 and 0.374
  • a. $$953$$; b. $$954$$ c. $$953.3$$ d. $$953.4$$
  • a. $$953$$; b. $$955$$ c. $$953.3$$ d. $$953.4$$
  • a. $$952$$; b. $$954$$ c. $$953.3$$ d. $$953.4$$
  • a. $$953$$; b. $$954$$ c. $$953.3$$ d. $$952.4$$
A physical quantity $$x$$ depends on quantities $$y$$ and $$z$$ as follows: $$x = Ay + B \tan (C_z)$$, where $$A, B$$ and $$C$$ are constants. Which of the followings do not have the same dimensions?
  • $$x$$ and $$B$$
  • $$C$$ and $$z^{-}$$
  • $$y$$ and $$B/A$$
  • $$x$$ and $$A$$
If $$L$$ and $$R$$ denote inductance and resistance, respectively, then the dimensions of $$L/R$$ are
  • $$M^1L^0T^0Q^{-1}$$
  • $$M^0L^0TQ^{0}$$
  • $$M^0L^1T^{-1}Q^{0}$$
  • $$M^{-1}LT^0Q^{-1}$$
In the relation $$\dfrac{dy}{dt} = 2 \omega \sin (\omega t + \phi_0)$$, the dimensional formula for $$\omega t + \phi_0$$ is
  • $$MLT$$
  • $$MLT^0$$
  • $$ML^0T^0$$
  • $$M^0L^0T^0$$
The following observations were taken for determining the surface tension of water by capillary tube method : diameter of capillary , $$D = 1.25 \times 10^{-2} m$$. Taking $$ g = 9.80 m s^{-2}$$ and using the relation $$T = (rgh/2) \times 10^3 Nm^{-1}$$. what is the possible error in measurement of surface tension T?
  • $$2.4\%$$
  • $$15\%$$
  • $$1.6\%$$
  • $$0.15\%$$
Write the dimensions of $$a \times b$$ in the relation. $$E = \dfrac{b - x^2}{at}$$, where $$E$$ is the energy, $$x$$ is the displacement, and $$t$$ is the time.
  • $$ML^2T$$
  • $$M^{-1}L^2T^1$$
  • $$ML^2T^{-2}$$
  • $$MLT^{-2}$$
The percentage errors in the measurement of mass and speed are $$2\%$$ and $$3\%$$, respectively. How much will be the maximum error in the estimation of KE obtained by measuring mass and speed?
  • $$5\%$$
  • $$1\%$$
  • $$8\%$$
  • $$11\%$$
If frequency $$F$$, velocity $$V$$, and density $$D$$ are considered fundamental units, the dimensional formula for momentum will be
  • $$DVF^2$$
  • $$DV^2F^{-1}$$
  • $$D^2V^2F^2$$
  • $$DV^4F^{-3}$$
If the velocity of light $$C$$, the universal gravitational constant $$G$$, and Planck's constant $$h$$ are chosen as fundamental units, the dimension of mass in this system are
  • $$h^{1/2}C^{1/2}G^{-1/2}$$
  • $$h^{-1}C^{-1}G$$
  • $$hCG^{-1}$$
  • $$hCG$$
Force F is given in terms of time t and distance x by $$F = A \sin Ct + B \cos Dx$$. Then the dimensions of $$\dfrac {A}{B}$$ and $$\dfrac{C}{D}$$ are:
  • $$[M^0L^0T^0], [M^0L^0T^{-1}]$$
  • $$[MLT^{-2}], [M^0L^{-1}T^{0}]$$
  • $$[M^0L^0T^0], [M^0LT^{-1}]$$
  • $$[M^0L^1T^{-1}], [M^0L^0T^0]$$
The number of significant figures in $$5.69 \times 10^{15}$$kg is
  • $$1$$
  • $$2$$
  • $$3$$
  • $$18$$
The radius of the earth is $$6.37 \times 10^6 m$$ and its mass is $$5.975 \times 10^{24} kg$$. Find the earth's average density to appropriate significant figures.
  • $$5 \times 10^3 kg m^{-3}$$
  • $$5.52 \times 10^3 kg m^{-3}$$
  • $$2 \times 10^3 kg m^{-3}$$
  • $$5.52 \times 10^3 kg m^{-4}$$
In the relation $$y = r sin (\omega t - kx)$$, the dimensions of $$\omega/k$$ are
  • $$[M^0L^0T^0]$$
  • $$[M^0L^{1}T^{-1}]$$
  • $$[M^0L^0T^1]$$
  • $$[M^0L^1T^0]$$
The time dependence of a physical quantity $$P$$ is given by $$P = P_0e^{-\alpha t^2}$$, where $$\alpha$$ is a constant and t is time. Then constant $$\alpha$$ is / has
  • Dimensionless
  • Dimensions of $$T^{-2}$$
  • Dimensions of P
  • Dimensions of $$T^{2}$$
The position x of a particle at time t is given by $$x = \dfrac{V_0}{a}(1 - e^{-at})$$, where $$V_0$$ is constant and $$a > 0$$. The dimensions of $$V_0$$ and $$a$$ are
  • $$M^0LT^{-1}$$ and $$T^{-1}$$
  • $$M^0LT^0$$ and $$T^{-1}$$
  • $$M^0LT^{-1}$$ and $$LT^{-2}$$
  • $$M^0LT^{-1}$$ and $$T$$
The mass of the liquid flowing per second per unit area of cross section of the tube if proportional to $$P^x$$ and $$v^y$$, where $$P$$ is the pressure difference and $$v$$ is the velocity then the relation between $$x$$ and $$y$$ is
  • $$x = y$$
  • $$x = - y$$
  • $$y^2 = x$$
  • $$y = -x^2$$
The Van der Waal's equation of state for some gases can be expressed as:
$$(P + \dfrac{a}{V^2})(V - b) = RT$$
where P is the pressure, V is the molar volume, and T is the absolute temperature of the given sample of gas and a,b and R are constants.
The dimensions of a are
  • $$ML^5T^{-2}$$
  • $$ML^{-1}T^{-2}$$
  • $$L^3$$
  • none of the above
In a given system of units, 1 unit of mass = 2 kg. 1 unit of length = 5 m and 1 unit of time = 5 sec. then in this system, 1 N represents:
  • 5/2 units of force
  • 2/5 units of force
  • 2 units of force
  • 1/2 units of force
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