A soap bubble of radius
Question: A soap bubble of radius $3 \mathrm{~cm}$ is formed inside the another soap bubble of radius $6 \mathrm{~cm}$. The radius of an equivalent soap bubble which has the same excess pressure as inside the smaller bubble with respect to the atmospheric pressure is $\ldots \ldots . \mathrm{cm}$. Solution: Excess pressure inside the smaller soap bubble $\Delta \mathrm{P}=\frac{4 \mathrm{~S}}{\mathrm{r}_{1}}+\frac{4 \mathrm{~S}}{\mathrm{r}_{2}}$ .........(I) The excess pressure inside the equiva...
Read More →The refractive index of a converging lens is 1.4.
Question: The refractive index of a converging lens is 1.4. What will be the focal length of this lens if it is placed in a medium of same refractive index ? (Assume the radii of curvature of the faces of lens are $R_{1}$ and $R_{2}$ respectively)1Infinite$\frac{\mathrm{R}_{1} \mathrm{R}_{2}}{\mathrm{R}_{1}-\mathrm{R}_{2}}$ZeroCorrect Option: , 2 Solution: $\frac{1}{\mathrm{~F}}=\left[\frac{\mu_{\mathrm{L}}}{\mu_{\mathrm{S}}}-1\right]\left[\frac{1}{\mathrm{R}_{1}}-\frac{1}{\mathrm{R}_{2}}\right]...
Read More →Two spherical balls having equal masses with radius of
Question: Two spherical balls having equal masses with radius of $5 \mathrm{~cm}$ each are thrown upwards along the same vertical direction at an interval of $3 \mathrm{~s}$ with the same initial velocity of $35 \mathrm{~m} / \mathrm{s}$, then these balls collide at a height of $\mathrm{m} .\left(\right.$ Take $\left.\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}\right)$ Solution: When both balls will collied $\mathrm{y}_{1}=\mathrm{y}_{2}$ $35 \mathrm{t}-\frac{1}{2} \times 10 \times \mathrm{t}^{2}=...
Read More →Calculate the value of mean free path
Question: Calculate the value of mean free path $(\lambda)$ for oxygen molecules at temperature $27^{\circ} \mathrm{C}$ and pressure $1.01 \times 10^{5} \mathrm{~Pa}$. Assume the molecular diameter $0.3 \mathrm{~nm}$ and the gas is ideal. $\left(\mathrm{k}=1.38 \times 10^{-23} \mathrm{JK}^{-1}\right)$ $\left(\mathrm{k}=1.38 \times 10^{-23} \mathrm{JK}^{-1}\right)$$58 \mathrm{~nm}$$32 \mathrm{~nm}$$86 \mathrm{~nm}$$102 \mathrm{~nm}$Correct Option: , 4 Solution: $\lambda=\frac{\mathrm{RT}}{\sqrt{2...
Read More →Electric field in a plane
Question: Electric field in a plane electromagnetic wave is given by $\mathrm{E}=50 \sin \left(500 \mathrm{x}-10 \times 10^{10} \mathrm{t}\right) \mathrm{V} / \mathrm{m}$ The velocity of electromagnetic wave in this medium is : (Given $\mathrm{C}=$ speed of light in vacuum)$\frac{3}{2} \mathrm{C}$$\mathrm{C}$$\frac{2}{3} \mathrm{C}$$\frac{C}{2}$Correct Option: , 3 Solution: $\mathrm{V}=\frac{\omega}{\mathrm{K}}=\frac{10 \times 10^{10}}{500}=2 \times 10^{8}$ $\mathbf{V}=\frac{2 \mathrm{C}}{3}$...
Read More →The angular momentum of a planet of mass
Question: The angular momentum of a planet of mass $M$ moving around the sun in an elliptical orbit is $\overrightarrow{\mathrm{L}}$. The magnitude of the areal velocity of the planet is:$\frac{4 L}{M}$$\frac{\mathrm{L}}{\mathrm{M}}$$\frac{2 L}{M} 80$$\frac{L}{2 M}$Correct Option: , 4 Solution: For small displacement ds of the planet its area can be written as $\mathrm{dA}=\frac{1}{2} \mathrm{rd} \ell$ $=\frac{1}{2} \mathrm{rds} \sin \theta$ A. vel $=\frac{\mathrm{dA}}{\mathrm{dt}}=\frac{1}{2} \...
Read More →The half-life
Question: The half-life of $\mathrm{Au}^{198}$ is $2.7$ days. The activity of $1.50 \mathrm{mg}$ of $\mathrm{Au}^{198}$ if its atomic weight i $198 \mathrm{~g} \mathrm{~mol}^{-1}$ is, $\left(\mathrm{N}_{\mathrm{A}}=6 \times 10^{23} / \mathrm{mol}\right)$$240 \mathrm{Ci}$$357 \mathrm{Ci}$$535 \mathrm{Ci}$$252 \mathrm{Ci}$Correct Option: , 2 Solution: $\mathrm{A}=\lambda \mathrm{N}$ $\mathrm{N}=\mathrm{nN}_{\mathrm{A}}$ $\left(\mathrm{t}_{1 / 2}=\frac{\ln 2}{\lambda}\right)$ $\mathrm{N}=\left(\fra...
Read More →A source and a detector move away from each other in absence of
Question: A source and a detector move away from each other in absence of wind with a speed of $20 \mathrm{~m} / \mathrm{s}$ with respect to the ground. If the detector detects a frequency of $1800 \mathrm{~Hz}$ of the sound coming from the source, then the original frequency of source considering speed of sound in air $340 \mathrm{~m} / \mathrm{s}$ will be $\mathrm{Hz}$ Solution: $f^{\prime}=f\left(\frac{C-V_{0}}{C+V_{s}}\right)$ $1800=f\left(\frac{340-20}{340+20}\right)$ $f=2025 \mathrm{~Hz}$ ...
Read More →In Millikan's oil drop
Question: In Millikan's oil drop experiment, what is viscous force acting on an uncharged drop of radius $2.0 \times 10^{-5} \mathrm{~m}$ and density $1.2 \times 10^{3} \mathrm{kgm}^{-3}$ ? Take viscosity of liquid $=1.8 \times 10^{-5} \mathrm{Nsm}^{-2}$. (Neglect buoyancy due to air).$3.8 \times 10^{-11} \mathrm{~N}$$3.9 \times 10^{-10} \mathrm{~N}$$1.8 \times 10^{-10} \mathrm{~N}$$5.8 \times 10^{-10} \mathrm{~N}$Correct Option: , 2 Solution: Viscous force $=$ Weight $=\rho \times\left(\frac{4}...
Read More →The electric field in a plane electromagnetic wave is given by
Question: The electric field in a plane electromagnetic wave is given by $\overrightarrow{\mathrm{E}}=200 \cos \left[\left(\frac{0.5 \times 10^{3}}{\mathrm{~m}}\right) \mathrm{x}-\left(1.5 \times 10^{11} \frac{\mathrm{rad}}{\mathrm{s}} \times \mathrm{t}\right)\right] \frac{\mathrm{V}}{\mathrm{m}} \hat{\mathrm{j}}$ If this wave falls normally on a perfectly reflecting surface having an area of $100 \mathrm{~cm}^{2}$. If the radiation pressure exerted by the E.M. wave on the surface during a 10 mi...
Read More →For the given circuit, comment on the type of transformer used :
Question: For the given circuit, comment on the type of transformer used : Auxilliary transformerAuto transformerStep-up transformerStep down transformerCorrect Option: Solution: $\mathrm{V}_{\mathrm{S}}=\frac{\mathrm{P}}{\mathrm{i}}=\frac{60}{0.11}=545.45$ $\mathrm{V}_{\mathrm{P}}=220$ $\mathrm{~V}_{\mathrm{S}}\mathrm{V}_{\mathrm{P}}$ $\Rightarrow$ Step up transformer...
Read More →Find the distance
Question: Find the distance of the image from object $\mathrm{O}$, formed by the combination of lenses in the figure : $75 \mathrm{~cm}$$10 \mathrm{~cm}$$20 \mathrm{~cm}$infinityCorrect Option: 1 Solution: $\frac{1}{V_{1}}+\frac{1}{30}=\frac{1}{10}$ $\frac{1}{V_{1}}=\frac{2}{30} \Rightarrow V_{1}=15 \mathrm{~cm}$ $\frac{1}{\mathrm{~V}_{2}}-\frac{1}{10}=-\frac{1}{10}$ $\frac{1}{\mathrm{~V}_{2}}=0 \quad \mathrm{~V}_{2}=\infty$ $\mathrm{V}_{3}=30 \mathrm{~cm}$ $\mathrm{OV}_{3}=75 \mathrm{~cm}$...
Read More →In a series LCR circuit, the inductive reactance
Question: In a series LCR circuit, the inductive reactance $\left(\mathrm{X}_{\mathrm{L}}\right)$ is $10 \Omega$ and the capacitive reactance $\left(\mathrm{X}_{\mathrm{C}}\right)$ is $4 \Omega$. The resistance (R) in the circuit is $6 \Omega$. The power factor of the circuit is :$\frac{1}{2}$$\frac{1}{2 \sqrt{2}}$$\frac{1}{\sqrt{2}}$$\frac{\sqrt{3}}{2}$Correct Option: , 3 Solution: We know that power factor is $\cos \phi$, $\cos \phi=\frac{R}{Z}$ ..........(1) $Z=\sqrt{R^{2}+\left(X_{L}-X_{C}\r...
Read More →The de-Broglie wavelength associated with an electron and a proton were calculated by
Question: The de-Broglie wavelength associated with an electron and a proton were calculated by accelerating them through same potential of $100 \mathrm{~V}$. What should nearly be the ratio of their wavelengths $?\left(\mathrm{~m}_{\mathrm{P}}=1.00727 \mathrm{u}, \mathrm{m}_{\mathrm{e}}=0.00055 \mathrm{u}\right)$$1860: 1$$(1860)^{2}: 1$$41.4: 1$$43: 1$Correct Option: , 4 Solution: $\lambda=\frac{h}{\mathrm{mv}}=\frac{\mathrm{h}}{\sqrt{2 \mathrm{mK}}}=\frac{\mathrm{h}}{\sqrt{2 \mathrm{mqV}}}$ $\...
Read More →Two ions of masses 4
Question: Two ions of masses 4 amu and 16 amu have charges $+2 \mathrm{e}$ and $+3 \mathrm{e}$ respectively. These ions pass through the region of constant perpendicular magnetic field. The kinetic energy of both ions is same. Then :lighter ion will be deflected less than heavier ionlighter ion will be deflected more than heavier ionboth ions will be deflected equallyno ion will be deflected.Correct Option: , 2 Solution: $\mathrm{r}=\frac{\mathrm{P}}{\mathrm{qB}}=\frac{\sqrt{2 \mathrm{mk}}}{\mat...
Read More →A uniform chain of length 3 meter and mass
Question: A uniform chain of length 3 meter and mass $3 \mathrm{~kg}$ overhangs a smooth table with 2 meter laying on the table. If $\mathrm{k}$ is the kinetic energy of the chain in joule as it completely slips off the table, then the value of $k$ is Solution: From energy conservation $\mathrm{K}_{\mathrm{i}}+\mathrm{U}_{\mathrm{i}}=\mathrm{k}_{\mathrm{f}}+\mathrm{U}_{\mathrm{f}}$ $0+\left(-1 \times 10 \times \frac{1}{2}\right)=\mathrm{k}_{\mathrm{f}}+\left(-3 \times 10 \times \frac{3}{2}\right...
Read More →The decay of a proton to neutron is :
Question: The decay of a proton to neutron is :not possible as proton mass is less than the neutron masspossible only inside the nucleusnot possible but neutron to proton conversion is possiblealways possible as it is associated only with $\beta^{+}$decayCorrect Option: , 2 Solution: It is possible only inside the nucleus and not otherwise....
Read More →Find out the surface charge density at the intersection of point x=3 m plane and $x$-axis,
Question: Find out the surface charge density at the intersection of point $x=3 \mathrm{~m}$ plane and $x$-axis, in the region of uniform line charge of $8 \mathrm{nC} /$ $m$ lying along the $z$-axis in free space.$0.424 \mathrm{nC} \mathrm{m}^{-2}$$47.88 \mathrm{C} / \mathrm{m}$$0.07 \mathrm{nC} \mathrm{m}^{-2}$$4.0 \mathrm{nC} \mathrm{m}^{-2}$Correct Option: 1 Solution: $\frac{2 \mathrm{~K} \lambda}{\mathrm{r}}=\frac{\sigma}{\varepsilon_{0}}$ $(x=3 m)$ $\sigma=0.424 \times 10^{-9} \frac{\mathr...
Read More →Solve this following
Question: Statement-I : By doping silicon semiconductor with pentavalent material, the electrons density increases. Statement-II : The n-type semiconductor has net negative charge. In the light of the above statements, choose the most appropriate answer from the options given below:Statement-I is true but Statement-II is false.Statement-I is false but Statement-II is true.Both Statement-I and Statement-II are true.Both Statement-I and Statement-II are false.Correct Option: 1 Solution: Pentavalen...
Read More →If the angular velocity of earth's spin is increased
Question: If the angular velocity of earth's spin is increased such that the bodies at the equator start floating, the duration of the day would be approximately : (Take : $\mathrm{g}=10 \mathrm{~ms}^{-2}$, the radius of earth, $\mathrm{R}=6400 \times 10^{3} \mathrm{~m}$, Take $\left.\pi=3.14\right)$60 minutesdoes not change1200 minutes84 minutesCorrect Option: , 4 Solution: For objects to float $m g=m \omega^{2} R$ $\omega=$ angular velocity of earth. $\mathrm{R}=$ Radius of earth $\omega=\sqrt...
Read More →A bar magnet is passing
Question: A bar magnet is passing through a conducting loop of radius $R$ with velocity $v$. The radius of the bar magnet is such that it just passes through the loop. The induced e.m.f. in the loop can be represented by the approximate curve : Correct Option: , 3 Solution: $\rightarrow$ When magnet passes through centre region of solenoid, no current / Emf is induced in loop. $\rightarrow$ While entering flux increases so negative induced emf $\rightarrow$ While leaving flux decreases so positi...
Read More →Find out the surface charge density at the intersection of point x=3m plane and $x$-axis,
Question: Find out the surface charge density at the intersection of point $x=3 \mathrm{~m}$ plane and $x$-axis, in the region of uniform line charge of $8 \mathrm{nC} /$ $m$ lying along the $z$-axis in free space.$0.424 \mathrm{nC} \mathrm{m}^{-2}$$47.88 \mathrm{C} / \mathrm{m}$$0.07 \mathrm{nC} \mathrm{m}^{-2}$$4.0 \mathrm{nC} \mathrm{m}^{-2}$Correct Option: Solution: $\frac{2 \mathrm{~K} \lambda}{\mathrm{r}}=\frac{\sigma}{\varepsilon_{0}}$ $(x=3 m)$ $\sigma=0.424 \times 10^{-9} \frac{\mathrm{...
Read More →In a photoelectric experiment,
Question: In a photoelectric experiment, increasing the intensity of incident light:increases the number of photons incident and also increases the K.E. of the ejected electronsincreases the frequency of photons incident and increases the K.E. of the ejected electrons.increases the frequency of photons incident and the K.E. of the ejected electrons remains unchangedincreases the number of photons incident and the K.E. of the ejected electrons remains unchangedCorrect Option: , 4 Solution: $\righ...
Read More →The material filled between the plates of a parallel plate capacitor has resistivity
Question: The material filled between the plates of a parallel plate capacitor has resistivity $200 \Omega \mathrm{m}$. The value of capacitance of the capacitor is $2 \mathrm{pF}$. If a potential difference of $40 \mathrm{~V}$ is applied across the plates of the capacitor, then the value of leakage current flowing out of the capacitor is : (given the value of relative permitivity of material is 50 )$9.0 \mu \mathrm{A}$$9.0 \mathrm{~mA}$$0.9 \mathrm{~mA}$$0.9 \mu \mathrm{A}$Correct Option: , 3 S...
Read More →Three rays of light, namely red (R),
Question: Three rays of light, namely red (R), green (G) and blue (B) are incident on the face $P Q$ of a right angled prism $\mathrm{PQR}$ as shown in figure. The refractive indices of the material of the prism for red, green and blue wavelength are $1.27,1.42$ and $1.49$ respectively. The colour of the ray(s) emerging out of the face PR is :greenredblue and greenblueCorrect Option: , 2 Solution: Assuming that the right angled prism is an isoceles prism, so the other angles will be $45^{\circ}$...
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