When a particle executes SHM,
Question: When a particle executes SHM, the nature of graphical representation of velocity as a function of displacement is :circularellipticalparabolicstraight lineCorrect Option: , 2 Solution: For a particle executing SHM, $x=A \sin (\omega t+\phi)$ $V=\omega A \cos (\omega t+\phi)$ $\Rightarrow \frac{\mathrm{v}^{2}}{\omega^{2} \mathrm{~A}^{2}}+\frac{\mathrm{x}^{2}}{\mathrm{~A}^{2}}=1 \Rightarrow$ equation of ellipse between $v$ and $x$ Hence option (2)...
Read More →In an octagon A B C D E F G H of equal side, what is the sum of
Question: In an octagon $A B C D E F G H$ of equal side, what is the sum of $-16 \hat{\mathrm{i}}-24 \hat{\mathrm{j}}+32 \hat{\mathrm{k}}$$16 \hat{\mathrm{i}}+24 \hat{\mathrm{j}}-32 \hat{\mathrm{k}}$$16 \hat{\mathrm{i}}+24 \hat{\mathrm{j}}+32 \hat{\mathrm{k}}$$16 \hat{\mathrm{i}}-24 \hat{\mathrm{j}}+32 \hat{\mathrm{k}}$Correct Option: , 2 Solution: We know, By triangle law of vector addition, we can write Now $\overrightarrow{\mathrm{AB}}+\overrightarrow{\mathrm{AC}}+\overrightarrow{\mathrm{AD}}...
Read More →Find the electric field at point P (as shown in figure) on the perpendicular
Question: Find the electric field at point P (as shown in figure) on the perpendicular bisector of a uniformly charged thin wire of length $L$ carrying a charge Q. The distance of the point $P$ from the centre of the rod is $a=\frac{\sqrt{3}}{2} L$. $\frac{\sqrt{3} Q}{4 \pi \varepsilon_{0} L^{2}}$$\frac{\mathrm{Q}}{3 \pi \varepsilon_{0} \mathrm{~L}^{2}}$$\frac{Q}{2 \sqrt{3} \pi \varepsilon_{0} L^{2}}$$\frac{Q}{4 \pi \varepsilon_{0} L^{2}}$Correct Option: , 3 Solution: $\mathrm{E}=\frac{\mathrm{k...
Read More →An unpolarized light
Question: An unpolarized light beam is incident on the polarizer of a polarization experiment and the intensity of light beam emerging from the analyzer is measured as 100 Lumens. Now, if the analyzer is rotated around the horizontal axis (direction of light) by $30^{\circ}$ in clockwise direction, the intensity of emerging light will be Lumens. Solution: Assuming initially axis of Polarizer and Analyzer are parallel Now emerging intensity $=\frac{\mathrm{I}_{0}}{2} \cos ^{2} 30^{\circ}$ $=100\l...
Read More →In a Young's double slit experiment two slits are separated
Question: In a Young's double slit experiment two slits are separated by $2 \mathrm{~mm}$ and the screen is placed one meter away. When a light of wavelength $500 \mathrm{~nm}$ is used, the fringe separation will be:$0.25 \mathrm{~mm}$$0.50 \mathrm{~mm}$$0.75 \mathrm{~mm}$$1 \mathrm{~mm}$Correct Option: 1 Solution: $\beta=\frac{\lambda \mathrm{D}}{\mathrm{d}}=\frac{500 \times 10^{-9} \times 1}{2 \times 10^{-3}}$ $\beta=\frac{5}{2} \times 10^{-4} \mathrm{~m}=2.5 \times 10^{-1} \mathrm{~mm}$ $\mat...
Read More →A common transistor radio
Question: A common transistor radio set requires $12 \mathrm{~V}$ (D.C.) for its operation. The D.C. source is constructed by using a transformer and a rectifier circuit, which are operated at $220 \mathrm{~V}$ (A.C.) on standard domestic A.C. supply. The number of turns of secondary coil are 24 , then the number of turns of primary are Solution: $\frac{N_{P}}{N_{S}}=\frac{V_{P}}{V_{S}}$ $\frac{N_{P}}{24}=\frac{220}{12}$ $N_{P}=\frac{220 \times 24}{12}$ $N_{P}=440$ Ans. 440 turns...
Read More →A ball will a speed of
Question: A ball will a speed of $9 \mathrm{~m} / \mathrm{s}$ collides with another identical ball at rest. After the collision, the direction of each ball makes an angle of $30^{\circ}$ with the original direction. The ratio of velocities of the balls after collision is $\mathrm{x}: \mathrm{y}$, where $x$ is Solution: From conservation of momentum along $y$-axis. $\vec{P}_{i y}=\vec{P}_{f y}$ $0+0=m v_{1} \sin 30^{\circ} \hat{\mathrm{j}}+\mathrm{mv}_{2} \sin 30^{\circ}(-\hat{\mathrm{j}})$ $\mat...
Read More →Four identical solid spheres each of mass 'm' and radius
Question: Four identical solid spheres each of mass 'm' and radius 'a' are placed with their centres on the four corners of a square of side ' $b$ '. The moment of inertia of the system about one side of square where the axis of rotation is parallel to the plane of the square is :$\frac{4}{5} m a^{2}+2 m b^{2}$$\frac{8}{5} \mathrm{ma}^{2}+\mathrm{mb}^{2}$$\frac{8}{5} m a^{2}+2 m b^{2}$$\frac{4}{5} \mathrm{ma}^{2}$Correct Option: , 3 Solution: $\mathrm{I}=2 \times\left(\frac{2}{5} \mathrm{ma}^{2}...
Read More →An audio signal
Question: An audio signal $v_{m}=20 \sin 2 \pi(1500 \mathrm{t})$ amplitude modulates a carrier $v_{C}=80 \sin 2 \pi(100,000 t)$ The value of percent modulation is Solution: $\%$ modulation $=\frac{\mathrm{Am}}{\mathrm{Ac}} \times 100$ $\%$ modulation $=\frac{20}{80} \times 100$ $\%$ modulation $=25 \%$ Ans 25...
Read More →In connection with the circuit drawn
Question: In connection with the circuit drawn below, the value of current flowing through $2 \mathrm{k} \Omega$ resistor is _________$\times 10^{-4} \mathrm{~A}$. Solution: Current through $2 \mathrm{k} \Omega$ resistance $\mathrm{I}=\frac{5}{2 \times 10^{3}}=2.5 \times 10^{-3} \mathrm{~A}$ $\mathrm{I}=25 \times 10^{-4} \mathrm{~A}$ Ans. 25...
Read More →An electromagnetic wave of frequency
Question: An electromagnetic wave of frequency $5 \mathrm{GHz}$, is travelling in a medium whose relative electric permittivity and relative magnetic permeability both are 2 . Its velocity in this medium is ____________ $\times 10^{7} \mathrm{~m} / \mathrm{s}$. Solution: Given : Frequency of wave $f=5 \mathrm{GHz}$ $=5 \times 10^{9} \mathrm{~Hz}$ Relative permittivity, $\in_{\mathrm{r}}=2$ and Relative permeability, $\mu_{\mathrm{r}}=2$ Since speed of light in a medium is given by, $\mathrm{v}=\...
Read More →An inclined plane is bent
Question: An inclined plane is bent in such a way that the vertical cross-section is given by $y=\frac{x^{2}}{4}$ where $\mathrm{y}$ is in vertical and $\mathrm{x}$ in horizontal direction. If the upper surface of this curved plane is rough with coefficient of friction $\mu=0.5$, the maximum height in $\mathrm{cm}$ at which a stationary block will not slip downward is Solution: At maximum ht. block will experience maximum friction force. Therefore if at this height slope of the tangent is $\tan ...
Read More →Two radioactive substances
Question: Two radioactive substances $\mathrm{X}$ and $\mathrm{Y}$ originally have $N_{1}$ and $N_{2}$ nuclei respectively. Half life of $X$ is half of the half life of $Y$. After three half lives of Y, number of nuclei of both are equal. The ratio $\frac{N_{1}}{N_{2}}$ will be equal to :$\frac{1}{8}$$\frac{3}{1}$$\frac{8}{1}$$\frac{1}{3}$Correct Option: , 3 Solution: $\mathrm{T}_{\mathrm{x}}=\mathrm{t} ; \mathrm{T}_{\mathrm{y}}=2 \mathrm{t}$ $3 \mathrm{~T}_{\mathrm{y}}=6 \mathrm{t}$ $\mathrm{N}...
Read More →A hydraulic press can
Question: A hydraulic press can lift $100 \mathrm{~kg}$ when a mass 'm' is placed on the smaller piston. It can lift $\mathrm{kg}$ when the diameter of the larger piston is increased by 4 times and that of the smaller piston is decreased by 4 times keeping the same mass ' $m$ ' on the smaller piston. Solution: Using Pascals law $\frac{100 \times \mathrm{g}}{\mathrm{A}_{2}}=\frac{\mathrm{mg}}{\mathrm{A}_{1}}$...(1) Let $m$ mass can lift $\mathrm{M}_{0}$ in second case then $\frac{\mathrm{M}_{0} \...
Read More →A solid sphere of radius R gravitationally attracts a particle
Question: A solid sphere of radius $R$ gravitationally attracts a particle placed at $3 R$ form its centre with a force $F_{1}$. Now a spherical cavity of radius $\left(\frac{\mathrm{R}}{2}\right)$ is made in the sphere (as shown in figure) and the force becomes $\mathrm{F}_{2}$. The value of $F_{1}: F_{2}$ is : $25: 36$$36: 25$$50: 41$$41: 50$Correct Option: , 3 Solution: Let initial mass of sphere is $\mathrm{m}^{\prime}$. Hence mass of removed portion will be $\mathrm{m}^{\prime} / 8$ $\mathr...
Read More →inductance and resistance $2 imes 10^{-4} mathrm{H}$ and $6.28 Omega$ respectively oscillates at $10 mathrm{MHz}$
Question: A resonance circuit having inductance and resistance $2 \times 10^{-4} \mathrm{H}$ and $6.28 \Omega$ respectively oscillates at $10 \mathrm{MHz}$ frequency. The value of quality factor of this resonator is__________ $[\pi=3.14]$ Solution: Given: $\mathrm{L}=2 \times 10^{-4} \mathrm{H}$ $\mathrm{R}=6.28 \Omega$ $\mathrm{f}=10 \mathrm{MHz}=10^{7} \mathrm{~Hz}$ Since quality factor, $\mathrm{Q}=\omega_{0} \frac{\mathrm{L}}{\mathrm{R}}=2 \pi \mathrm{f} \frac{\mathrm{L}}{\mathrm{R}}$ $\ther...
Read More →Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R.
Question: Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R. Assertion A : Body 'P' having mass M moving with speed 'u' has head-on collision elastically with another body ' $Q$ ' having mass ' $m$ ' initially at rest. If $\mathrm{m}\mathrm{M}$, body ' $Q$ ' will have a maximum speed equal to '2u' after collision. Reason R : During elastic collision, the momentum and kinetic energy are both conserved. In the light of the above statements, choos...
Read More →The coefficient of static friction
Question: The coefficient of static friction between a wooden block of mass $0.5 \mathrm{~kg}$ and a vertical rough wall is $0.2$. The magnitude of horizontal force that should be applied on the block to keep it adhere to the wall will be $\mathrm{N}$. $\left[\mathrm{g}=10 \mathrm{~ms}^{-2}\right.$ ] Solution: F.B.D. of the block is shown in the diagram Since block is at rest therefore $\mathrm{fr}-\mathrm{mg}=0$..(1) $\mathrm{F}-\mathrm{N}=0$..(2) $\mathrm{fr} \leq \mu \mathrm{N}$ In limiting c...
Read More →Magnetic fields at two points on the axis of a circular
Question: Magnetic fields at two points on the axis of a circular coil at a distance of $0.05 \mathrm{~m}$ and $0.2 \mathrm{~m}$ from the centre are in the ratio $8: 1$. The radius of coil is_________.$0.2 \mathrm{~m}$$0.1 \mathrm{~m}$$0.15 \mathrm{~m}$$1.0 \mathrm{~m}$Correct Option: , 2 Solution: We know, the magnetic field on the axis of a current carrying circular ring is given by $\mathrm{B}=\frac{\mu_{0}}{4 \pi} \frac{2 \mathrm{NIA}}{\left(\mathrm{R}^{2}+\mathrm{x}^{2}\right)^{3 / 2}}$ $\t...
Read More →The workdone by a gas molecule in an isolated
Question: The workdone by a gas molecule in an isolated system is given by, $\mathrm{W}=\alpha \beta^{2} \mathrm{e}^{-\frac{x^{2}}{\alpha k T}}$, where $\mathrm{x}$ is the displacement, $\mathrm{k}$ is the Boltzmann constant and $\mathrm{T}$ is the temperature, $\alpha$ and $\beta$ are constants. Then the dimension of $\beta$ will be :$\left[\mathrm{M} \mathrm{L}^{2} \mathrm{~T}^{-2}\right]$$\left[\mathrm{M} \mathrm{L} \mathrm{} \mathrm{T}^{-2}\right]$$\left[\mathrm{M}^{2} \mathrm{~L} \mathrm{~T...
Read More →Match List-I with List-II :
Question: Match List-I with List-II : Choose the correct answer from the options given below:(a) $\rightarrow$ (iii), (b) $\rightarrow$ (iv), (c) $\rightarrow($ ii ), (d) $\rightarrow$ (i)(a) $\rightarrow$ (ii), (b) $\rightarrow$ (iii), (c) $\rightarrow$ (iv), (d) $\rightarrow$ (i)(a) $\rightarrow$ (i), (b) $\rightarrow$ (ii), (c) $\rightarrow$ (iv), (d) $\rightarrow$ (iii)(a) $\rightarrow$ (iii), (b) $\rightarrow$ (ii), (c) $\rightarrow$ (iv), (d) $\rightarrow$ (i)Correct Option: , 2 Solution: ...
Read More →Consider two satellites
Question: Consider two satellites $S_{1}$ and $S_{2}$ with periods of revolution $1 \mathrm{hr}$. and $8 \mathrm{hr}$. respectively revolving around a planet in circular orbits. The ratio of angular velocity of satellite $S_{1}$ to the angular velocity of satellites $S_{2}$ is :$8: 1$$1: 4$$2: 1$$1: 8$Correct Option: 1 Solution: $\frac{\mathrm{T}_{1}}{\mathrm{~T}_{2}}=\frac{1}{8}$ $\frac{2 \pi / \omega_{1}}{2 \pi / \omega_{2}}=\frac{1}{8}$ $\frac{\omega_{1}}{\omega_{2}}=\frac{8}{1}$...
Read More →A planet revolving in elliptical orbit has:
Question: A planet revolving in elliptical orbit has : (A) a constant velocity of revolution. (B) has the least velocity when it is nearest to the sun. (C) its areal velocity is directly proportional to its velocity. (D) areal velocity is inversely proportional to its velocity. (E) to follow a trajectory such that the areal velocity is constant. Choose the correct answer from the options given below :A onlyD onlyC onlyE onlyCorrect Option: , 4 Solution: As per Keppler's $2^{\text {nd }}$ law, Ar...
Read More →A cube of side 'a'
Question: A cube of side 'a' has point charges $+Q$ located at each of its vertices except at the origin where the charge is $-\mathrm{Q}$. The electric field at the centre of cube is : $\frac{-\mathrm{Q}}{3 \sqrt{3} \pi \varepsilon_{0} \mathrm{a}^{2}}(\hat{\mathrm{x}}+\hat{\mathrm{y}}+\hat{\mathrm{z}})$$\frac{-2 Q}{3 \sqrt{3} \pi \varepsilon_{0} a^{2}}(\hat{x}+\hat{y}+\hat{z})$$\frac{2 \mathrm{Q}}{3 \sqrt{3} \pi \varepsilon_{0} \mathrm{a}^{2}}(\hat{\mathrm{x}}+\hat{\mathrm{y}}+\hat{\mathrm{z}})...
Read More →A cell
Question: A cell $\mathrm{E}_{1}$ of emf $6 \mathrm{~V}$ and internal resistance $2 \Omega$ is connected with another cell $E_{2}$ of emf $4 \mathrm{~V}$ and internal resistance $8 \Omega$ (as shown in the figure). The potential difference across points $X$ and $Y$ is : $10.0 \mathrm{~V}$$3.6 \mathrm{~V}$$5.6 \mathrm{~V}$$2.0 \mathrm{~V}$Correct Option: , 3 Solution: $I=\frac{6-4}{10}=\frac{1}{5} \mathrm{~A}$ $\mathrm{V}_{\mathrm{x}}+4+8 \times \frac{1}{5}-\mathrm{V}_{\mathrm{y}}=0$ $\mathrm{V}_...
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