A polyatomic ideal gas
Question: A polyatomic ideal gas has 24 vibrational modes. What is the value of $\gamma$ ?1.031.301.3710.3Correct Option: 1 Solution: Since each vibrational mode has 2 degrees of freedom hence total vibrational degrees of freedom $=48$ $f=3+3+48=54$ $\gamma=1+\frac{2}{f}=\frac{28}{27}=1.03$...
Read More →When two soap bubbles
Question: When two soap bubbles of radii a and $b$ ( $b$ a) coalesce, the radius of curvature of common surface is :$\frac{a b}{b-a}$$\frac{a+b}{a b}$$\frac{b-a}{a b}$$\frac{a b}{a+b}$Correct Option: 1 Solution: Excess pressure at common surface is given by $\mathrm{P}_{\mathrm{ex}}=4 \mathrm{~T}\left(\frac{1}{\mathrm{a}}-\frac{1}{\mathrm{~b}}\right)=\frac{4 \mathrm{~T}}{\mathrm{r}}$ $\therefore \frac{1}{\mathrm{r}}=\frac{1}{\mathrm{a}}-\frac{1}{\mathrm{~b}}$ $\mathrm{r}=\frac{\mathrm{ab}}{\math...
Read More →An aeroplane, with its wings spread
Question: An aeroplane, with its wings spread $10 \mathrm{~m}$, is flying at a speed of $180 \mathrm{~km} / \mathrm{h}$ in a horizontal direction. The total intensity of earth's field at that part is $2.5 \times 10^{-4} \mathrm{~Wb} / \mathrm{m}^{2}$ and the angle of dip is $60^{\circ}$. The emf induced between the tips of the plane wings will be :- $108.25 \mathrm{mV}$$54.125 \mathrm{mV}$$88.37 \mathrm{mV}$$62.50 \mathrm{mV}$Correct Option: 1 Solution: $\epsilon=[\overrightarrow{\mathrm{B}} \ov...
Read More →A triangular plate is shown.
Question: A triangular plate is shown. A force $\overrightarrow{\mathrm{F}}=4 \hat{\mathrm{i}}-3 \hat{\mathrm{j}}$ is applied at point $\mathrm{P}$. The torque at point $\mathrm{P}$ with respect to point ' $O^{\prime}$ and ' $Q$ ' are : $-15-20 \sqrt{3}, 15-20 \sqrt{3}$$15+20 \sqrt{3}, 15-20 \sqrt{3}$$15-20 \sqrt{3}, 15+20 \sqrt{3}$$-15+20 \sqrt{3}, 15+20 \sqrt{3}$Correct Option: 1 Solution: $\overrightarrow{\mathrm{F}}=4 \hat{\mathrm{i}}-3 \hat{\mathrm{j}}$ $\overrightarrow{\mathrm{r}}_{1}=5 \h...
Read More →Solve this following
Question: The length of metallic wire is $\ell_{1}$ when tension in it is $T_{1}$. It is $\ell_{2}$ when the tension is $T_{2}$. The original length of the wire will be -$\frac{\ell_{1}+\ell_{2}}{2}$$\frac{\mathrm{T}_{2} \ell_{1}+\mathrm{T}_{1} \ell_{2}}{\mathrm{~T}_{1}+\mathrm{T}_{2}}$$\frac{\mathrm{T}_{2} \ell_{1}-\mathrm{T}_{1} \ell_{2}}{\mathrm{~T}_{2}-\mathrm{T}_{1}}$$\frac{\mathrm{T}_{1} \ell_{1}-\mathrm{T}_{2} \ell_{2}}{\mathrm{~T}_{2}-\mathrm{T}_{1}}$Correct Option: , 3 Solution: Assumin...
Read More →Solve this following
Question: If ' $C^{\prime}$ and ' $V^{\prime}$ represent capacity and voltage respectively then what are the dimensions of $\lambda$, where $\frac{\mathrm{C}}{\mathrm{V}}=\lambda$ ?$\left[\mathrm{M}^{-2} \mathrm{~L}^{-3} \mathrm{I}^{2} \mathrm{~T}^{6}\right]$$\left[\mathrm{M}^{-3} \mathrm{~L}^{-4} \mathbf{I}^{3} \mathrm{~T}^{7}\right]$$\left[\mathrm{M}^{-1} \mathrm{~L}^{-3} \mathrm{I}^{-2} \mathrm{~T}^{-7}\right]$$\left[\mathrm{M}^{-2} \mathrm{~L}^{-4} \mathrm{I}^{3} \mathrm{~T}^{7}\right]$Corre...
Read More →An LCR circuit contains resistance of
Question: An LCR circuit contains resistance of $110 \Omega$ and a supply of $220 \mathrm{~V}$ at $300 \mathrm{rad} / \mathrm{s}$ angular frequency. If only capacitance is removed from the circuit, current lags behind the voltage by $45^{\circ}$. If on the other hand, only inductor is removed the current leads by $45^{\circ}$ with the applied voltage. The rms current flowing in the circuit will be :$1 \mathrm{~A}$$2.5 \mathrm{~A}$$1.5 \mathrm{~A}$$2 \mathrm{~A}$Correct Option: , 4 Solution: $\ta...
Read More →An electromagnetic wave
Question: An electromagnetic wave of frequency $3 \mathrm{GHz}$ enters a dielectric medium of relative electric permittivity $2.25$ from vacuum. The wavelength of this wave in that medium will be ___________$\times 10^{-2} \mathrm{~cm}$. Solution: $\lambda$ in vacuum $=\frac{\mathrm{c}}{\mathrm{f}}=\frac{3 \times 10^{8}}{3 \times 10^{9}}=0.1 \mathrm{~m}$ $\therefore \lambda$ in medium $=\frac{0.1}{\mu}$ Where refractive index $\mu=\sqrt{\mu_{r} \varepsilon_{r}}$ Assuming non-magnetic material $\...
Read More →The wavelength of the photon emitted by
Question: The wavelength of the photon emitted by a hydrogen atom when an electron makes a transition from $\mathrm{n}=2$ to $\mathrm{n}=1$ state is :$194.8 \mathrm{~nm}$$913.3 \mathrm{~nm}$$490.7 \mathrm{~nm}$$121.8 \mathrm{~nm}$Correct Option: , 4 Solution: $\frac{1}{\lambda}=\mathrm{R}\left(\frac{1}{1^{2}}-\frac{1}{2^{2}}\right)$ $\lambda=121.8 \mathrm{~nm} .$...
Read More →Two cars are approaching
Question: Two cars are approaching each other at an equal speed of $7.2 \mathrm{~km} / \mathrm{hr}$. When they see each other, both blow horns having frequency of $676 \mathrm{~Hz}$. The beat frequency heard by each driver will be ____________$\mathrm{Hz}$. [Velocity of sound in air is 340 $\mathrm{m} / \mathrm{s} .]$ Solution: Frequency of sound heard by car- 1 , which comes by reflection from car- 2 $\mathrm{f}_{1}=\mathrm{f}_{0}\left(\frac{340+2}{340-2}\right)\left(\frac{340+2}{340-2}\right)$...
Read More →A person standing on a spring balance inside a stationary
Question: A person standing on a spring balance inside a stationary lift measures $60 \mathrm{~kg}$. The weight of that person if the lift descends with uniform downward acceleration of $1.8 \mathrm{~m} / \mathrm{s}^{2}$ will be_ $\mathrm{N}$. $\left[\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}\right]$ Solution: When lift is at rest $\mathrm{N}=\mathrm{mg}$ $\Rightarrow 60 \times 10=600 \mathrm{~N}$ When lift moves with downward acceleration. In frame of lift pseudo force will be in upward directi...
Read More →A series LCR circuit
Question: A series LCR circuit is designed to resonate at an angular frequency $\omega_{0}=10^{5} \mathrm{rad} / \mathrm{s}$. The circuit draws $16 \mathrm{~W}$ power from $120 \mathrm{~V}$ source at resonance. The value of resistance ' $R$ ' in the circuit is ________$\Omega$. Solution: At resonance $\mathrm{P}=\frac{\mathrm{V}^{2}}{\mathrm{R}}$ $\mathrm{R}=\frac{\mathrm{V}^{2}}{\mathrm{P}}=\frac{(120)^{2}}{16}$ $=900 \Omega$...
Read More →A charge ' q' is placed at one corner of a cube
Question: A charge ' $q$ ' is placed at one corner of a cube as shown in figure.The flux of electrostatic field $\vec{E}$ through the shaded area is: $\frac{q}{4 \varepsilon_{0}}$$\frac{q}{24 \varepsilon_{0}}$$\frac{q}{48 \varepsilon_{0}}$$\frac{q}{8 \varepsilon_{0}}$Correct Option: , 2 Solution: flux through cube $=\frac{\mathrm{q}}{8 \epsilon_{0}}$ flux through surfaces $\mathrm{ABEH}, \mathrm{ADGH}, \mathrm{ABCD}$ will be zero $\phi(\mathrm{EFGH})=\phi(\mathrm{DCFG})=\phi(\mathrm{EBCF})=\frac...
Read More →The maximum and minimum amplitude of an amplitude modulated wave is
Question: The maximum and minimum amplitude of an amplitude modulated wave is $16 \mathrm{~V}$ and $8 \mathrm{~V}$ respectively. The modulation index for this amplitude modulated wave is $x \times 10^{-2}$. The value of $x$ is Solution: Modulation index $=\frac{A_{\max }-A_{\min }}{A_{\max }+A_{\min }}$ $=\frac{16-8}{16+8}=\frac{8}{24}=\frac{1}{3}=0.33$ $x \times 10^{-2}=0.33$ $x=33$...
Read More →A signal of
Question: A signal of $0.1 \mathrm{~kW}$ is transmitted in a cable. The attenuation of cable is $-5 \mathrm{~dB}$ per km and cable length is $20 \mathrm{~km}$. The power received at receiver is $10^{-x} \mathrm{~W}$. The value of $\mathrm{x}$ is _________ [Gain in $\mathrm{dB}=10 \log _{10}\left(\frac{\mathrm{P}_{0}}{\mathrm{P}_{i}}\right)$ ] Solution: Sound level decreases by $5 \mathrm{~dB}$ every $\mathrm{km}$ so sound level decreased in $20 \mathrm{~km}=100 \mathrm{~dB}$ $\beta_{2}-\beta_{1}...
Read More →If a message signal of frequency
Question: If a message signal of frequency ' $f_{\mathrm{m}}$ ' is amplitude modulated with a carrier signal of frequency ' $f$ c ' and radiated through an antenna, the wavelength of the corresponding signal in air is:$\frac{\mathrm{c}}{f_{\mathrm{c}}-f_{\mathrm{m}}}$$\frac{\mathrm{c}}{f_{\mathrm{m}}}$$\frac{\mathrm{c}}{f_{\mathrm{c}}+f_{\mathrm{m}}}$$\frac{\mathrm{c}}{f_{\mathrm{c}}}$Correct Option: , 4 Solution: (4) $\lambda=\frac{V}{f}=\frac{c}{f_{c}}$...
Read More →In a series LCR resonant circuit, the quality factor is measured as 100 .
Question: In a series LCR resonant circuit, the quality factor is measured as 100 . If the inductance is increased by two fold and resistance is decreased by two fold, then the quality factor after this change will be Solution: $\mathrm{Q}=\frac{\mathrm{X}_{\mathrm{L}}}{\mathrm{R}}=\frac{\omega \mathrm{L}}{\mathrm{R}}=\frac{1}{\sqrt{\mathrm{LC}}} \frac{\mathrm{L}}{\mathrm{R}}=\frac{\sqrt{\mathrm{L}}}{\mathrm{R} \sqrt{\mathrm{C}}}$ $Q^{\prime}=\frac{\sqrt{2 L}}{\left(\frac{R}{2}\right) \sqrt{C}}=...
Read More →A point charge
Question: A point charge of $+12 \mu \mathrm{C}$ is at a distance $6 \mathrm{~cm}$ vertically above the centre of a square of side $12 \mathrm{~cm}$ as shown in figure. The magnitude of the electric flux through the square will be ____________$\times 10^{3} \mathrm{Nm}^{2} / \mathrm{C}$. Solution: From symmetry $\phi=\frac{1}{6}\left(\frac{\mathrm{q}}{\varepsilon_{0}}\right)$ $=\frac{12 \times 10^{-6}}{6 \times 8.85 \times 10^{-12}}$ $=225.98 \times 10^{3} \frac{\mathrm{Nm}^{2}}{\mathrm{~s}}$ $\...
Read More →The root mean square
Question: The root mean square speed of molecules of a given mass of a gas at $27^{\circ} \mathrm{C}$ and 1 atmosphere pressure is $200 \mathrm{~ms}^{-1}$. The root mean square speed of molecules of the gas at $127^{\circ} \mathrm{C}$ and 2 atmosphere pressure is $\frac{x}{\sqrt{3}} \mathrm{~ms}^{-1}$. The value of $x$ will be Solution: $\mathrm{v}_{\mathrm{rms}}=\sqrt{\frac{3 \mathrm{RT}}{\mathrm{M}}}$ $\mathrm{v}_{\mathrm{rms}} \propto \sqrt{\mathrm{T}}$ $\frac{\left(\mathrm{v}_{\mathrm{rms}}\...
Read More →Two identical springs of spring constant '
Question: Two identical springs of spring constant ' $2 \mathrm{k}$ ' are attached to a block of mass $m$ and to fixed support (see figure).When the mass is displaced from equilibrium position on either side, it executes simple harmonic motion. The time period of oscillations of this sytem is: $2 \pi \sqrt{\frac{m}{k}}$$\pi \sqrt{\frac{m}{2 k}}$$2 \pi \sqrt{\frac{m}{2 k}}$$\pi \sqrt{\frac{\mathrm{m}}{\mathrm{k}}}$Correct Option: 4, Solution: (4) For parallel combination $k_{e q}=k_{1}+k_{2}$ $\m...
Read More →Two solids
Question: Two solids $\mathrm{A}$ and $\mathrm{B}$ of mass $1 \mathrm{~kg}$ and $2 \mathrm{~kg}$ respectively are moving with equal linear momentum. The ratio of their kinetic energies $(\text { K.E. })_{\mathrm{A}}:(\text { K.E. })_{\mathrm{B}}$ will be $\frac{\mathrm{A}}{1}$, so the value of $\mathrm{A}$ will be Solution: Kinetic energy $\mathrm{K}=\frac{\mathrm{P}^{2}}{2 \mathrm{~m}},\left(\mathrm{P}_{\mathrm{A}}=\mathrm{P}_{\mathrm{B}}\right)$ $K \propto \frac{1}{m}$ $\frac{\mathrm{K}_{\math...
Read More →Given below are two statements :
Question: Given below are two statements : Statement I : In a diatomic molecule, the rotational energy at a given temperature obeys Maxwell's distribution. Statement II : In a diatomic molecule, the rotational energy at a given temperature equals the translational kinetic energy for each molecule. In the light of the above statements, choose the correct answer from the options given below :Statement I is false but Statement II is true.Both Statement I and Statement II are false.Both Statement I ...
Read More →A uniform thin bar
Question: A uniform thin bar of mass $6 \mathrm{~kg}$ and length $2.4$ meter is bent to make an equilateral hexagon. The moment of inertia about an axis passing through the centre of mass and perpendicular to the plane of hexagon is _____________ $\times 10^{-1} \mathrm{~kg} \mathrm{~m}^{2}$. Solution: $61=2.4 \ell=0.4 \mathrm{~m}$ $\sin 60^{\circ}=\frac{r}{\ell}$ $r=1 \sin 60^{\circ}=\frac{\ell \sqrt{3}}{2}$ MOI, $\quad \mathrm{I}=\left[\frac{\mathrm{m} \ell^{2}}{12}+\mathrm{mr}^{2}\right] 6$ $...
Read More →A cylindrical wire of
Question: A cylindrical wire of radius $0.5 \mathrm{~mm}$ and conductivity $5 \times 10^{7} \mathrm{~S} / \mathrm{m}$ is subjected to an electric field of $10 \mathrm{mV} / \mathrm{m}$. The expected value of current in the wire will be $x^{3} \pi \mathrm{mA}$. The value of $x$ is Solution: Conductivity $\sigma=5 \times 10^{7} \mathrm{~S} / \mathrm{m}$ Radius $\mathrm{r}=0.5 \mathrm{~mm}=5 \times 10^{-4} \mathrm{~m}$ $\mathrm{E}=10 \times 10^{-3} \frac{\mathrm{V}}{\mathrm{m}}$ $J=\sigma E=10 \tim...
Read More →A stone is dropped from the top of a building.
Question: A stone is dropped from the top of a building. When it crosses a point $5 \mathrm{~m}$ below the top, another stone starts to fall from a point $25 \mathrm{~m}$ below the top. Both stones reach the bottom of building simultaneously. The height of the building is :$35 \mathrm{~m}$$45 \mathrm{~m}$$50 \mathrm{~m}$$25 \mathrm{~m}$Correct Option: , 2 Solution: Time for particle to meet $=\mathrm{t}^{\prime}=\frac{\mathrm{S}_{\mathrm{rel}}}{\mathrm{S}_{\mathrm{rel}}}=\frac{20}{10}=2 \mathrm{...
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