Unit and Measurement MCQ Questions & Answers in Basic Physics | Physics
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21.
Intensity observed in an interference pattern is $$I = {I_0}{\sin ^2}\theta .$$ At $$\theta = {30^ \circ }$$ intensity $$I = 5 \pm 0.0020\,W/{m^2}.$$ Find percentage error in angle if $${I_0} = 20\,W/{m^2}.$$
22.
The unit of the Stefan-Boltzmann's constant is
A
$$\frac{W}{{{m^2}{K^4}}}$$
B
$$\frac{W}{{{m^2}}}$$
C
$$\frac{W}{{{m^2}K}}$$
D
$$\frac{W}{{{m^2}{K^2}}}$$
Answer :
$$\frac{W}{{{m^2}{K^4}}}$$
$$E = \sigma A{T^4}$$
$$E$$ is energy dissipated per second.
$$\sigma = \frac{E}{{A{T^4}}} = \frac{{{\text{Watt}}}}{{{m^2}{K^4}}}$$
23.
Suppose the kinetic energy of a body oscillating with amplitude $$A$$ and at a distance $$x$$ is given by
$$K = \frac{{Bx}}{{{x^2} + {A^2}}}$$
The dimensions of $$B$$ are the same as that of
From $$K = \frac{{Bx}}{{{x^2} + {A^2}}} = \frac{{Bx}}{{{x^2}}} = \frac{B}{x}$$
$$\eqalign{
& \therefore B = K \times x = K.E. \times {\text{distance}} \cr
& = {\text{work}} \times {\text{distance}} \cr} $$
24.
The dimensional formula for relative density is
A
$$\left[ {M{L^{ - 3}}} \right]$$
B
$$\left[ {{M^o}{L^{ - 3}}} \right]$$
C
$$\left[ {{M^o}{L^o}{T^{ - 1}}} \right]$$
D
$$\left[ {{M^o}{L^o}{T^o}} \right]$$
Answer :
$$\left[ {{M^o}{L^o}{T^o}} \right]$$
Relative density $$ = \frac{{{\text{Density of Substance}}}}{{{\text{Density of water}}}}$$
Hence no dimension.
25.
Which of the following is a dimensional constant?
A
Refractive index
B
Poisson’s ratio
C
Relative density
D
Gravitational constant
Answer :
Gravitational constant
A quantity which has dimensions and also has a constant value is called dimensional constant. Here, gravitational constant $$\left( G \right)$$ is a dimensional constant.
26.
The density of a cube is measured by measuring its mass and length of its sides. If the maximum error in the measurement of mass and length are $$4\% $$ and $$3\% $$ respectively, the maximum error in the measurement of density will be
$$\eqalign{
& {\text{According to Coulomb's law, the electrostatic force}} \cr
& F = \frac{1}{{4\pi {\varepsilon _0}}} \times \frac{{{q_1}{q_2}}}{{{r^2}}} \cr
& {q_1}\,{\text{and }}{q_2}\, = {\text{charges, }}r = {\text{distance between charges}} \cr
& {\text{and}}\,{\varepsilon _0} = \,{\text{permittivity of free space}} \cr
& \Rightarrow {\varepsilon _0} = \frac{1}{{4\pi }} \times \frac{{{q_1}{q_2}}}{{{r^2}F}} \cr
& {\text{Substituting the units for }}q,r{\text{ and }}F,\,{\text{we obtain unit}}\,{\text{of}}\,{\varepsilon _0} \cr
& = \frac{{{\text{coulomb}} \times {\text{coulomb}}}}{{{\text{newton}} - {{\left( {{\text{metre}}} \right)}^2}}} \cr
& = \frac{{{{\left( {{\text{coulomb}}} \right)}^2}}}{{{\text{newton}} - {{\left( {{\text{metre}}} \right)}^2}}} \cr} $$
28.
The following observations were taken for determining surface tension $$T$$ of water by capillary method:
Diameter of capillary, $$D = 1.25 \times {10^{ - 2}}m$$
Rise of water, $$h = 1.45 \times {10^{ - 2}}m$$
Using $$g = 9.80\,m/{s^2}$$ and the simplified relation $$T = \frac{{rgh}}{2} \times {10^3}N/m,$$ the possible error in surface tension is closest to-
29.
A physical quantity $$A$$ is related to four observable quantities $$a, b, c$$ and $$d$$ as follows, $$A = \frac{{{a^2}{b^3}}}{{c\sqrt d }}$$ and the percentage errors of measurement in $$a, b, c$$ and dare $$1\% ,3\% ,2\% $$ and $$2\% $$ respectively. What is the percentage error in the quantity $$A$$?
30.
Write the dimensions of $$a \times b$$ in the relation $$E = \frac{{b - {x^2}}}{{at}},$$ Where $$E$$ is the energy, $$x$$ is the displacement and $$t$$ is time
A
$$M{L^2}T$$
B
$${M^{ - 1}}{L^2}{T^1}$$
C
$$M{L^2}{T^{ - 2}}$$
D
$$ML{T^{ - 2}}$$
Answer :
$${M^{ - 1}}{L^2}{T^1}$$
Here, $$b$$ and $${x^2} = {L^2}$$ have same dimensions
Also, $$a = \frac{{{x^2}}}{{E \times t}} = \frac{{{L^2}}}{{\left( {M{L^2}{T^{ - 2}}} \right)T}} = {M^{ - 1}}{T^1}$$
$$a \times b = \left[ {{M^{ - 1}}{L^2}{T^1}} \right]$$