Two concentric circular coils,
Question: Two concentric circular coils, $\mathrm{C}_{1}$ and $\mathrm{C}_{2}$, are placed in the $X Y$ plane. $C_{1}$ has 500 turns, and a radius of $1 \mathrm{~cm} . \mathrm{C}_{2}$ has 200 turns and radius of $20 \mathrm{~cm} . \mathrm{C}_{2}$ carries a time dependent current $\mathrm{I}(\mathrm{t})=\left(5 \mathrm{t}^{2}-2 \mathrm{t}+3\right) \mathrm{A}$ where $\mathrm{t}$ is in $\mathrm{s}$. The emf induced in $\mathrm{C}_{1}$ (in $\mathrm{mV}$ ), at the instant $\mathrm{t}=1 \mathrm{~s}$ i...
Read More →A screw gauge has 50 divisions on its circular scale.
Question: A screw gauge has 50 divisions on its circular scale. The circular scale is 4 units ahead of the pitch scale marking, prior to use. Upon one complete rotation of the circular scale, a displacement of $0.5 \mathrm{~mm}$ is noticed on the pitch scale. The nature of zero error involved, and the least count of the screw gauge, are respectively : Negative, $2 \mu \mathrm{m}$Positive, $10 \mu \mathrm{m}$Positive, $0.1 \mu \mathrm{m}$Positive, $0.1 \mathrm{~mm}$Correct Option: , 2 Solution: L...
Read More →Two capacitors of capacitances
Question: Two capacitors of capacitances $\mathrm{C}$ and $2 \mathrm{C}$ are charged to potential differences $\mathrm{V}$ and $2 \mathrm{~V}$, respectively. These are then connected in parallel in such a manner that the positive terminal of one is connected to the negative terminal of the other. The final energy of this configuration is:$\frac{9}{2} \mathrm{CV}^{2}$$\frac{25}{6} \mathrm{CV}^{2}$Zero$\frac{3}{2} \mathrm{CV}^{2}$Correct Option: , 4 Solution: $\Rightarrow$ By conservation of charg...
Read More →In the circuit, given in the figure currents in different
Question: In the circuit, given in the figure currents in different branches and value of one resistor are shown. Then potential at point $\mathrm{B}$ with respect to the point $\mathrm{A}$ is : + 1V$-1 \mathrm{~V}$$-2 \mathrm{~V}$$+2 \mathrm{~V}$Correct Option: 1 Solution: Let us asssume the potential at $\mathrm{A}=\mathrm{V}_{\mathrm{A}}=0$ Now at junction $\mathrm{C}$, According to $\mathrm{KCL}$ $\mathrm{i}_{1}+\mathrm{i}_{3}=\mathrm{i}_{2}$ $1 \mathrm{~A}+\mathrm{i}_{3}=2 \mathrm{~A}$ $\ma...
Read More →Solve this following
Question: Charges $\mathrm{Q}_{1}$ and $\mathrm{Q}_{2}$ arc at points $\mathrm{A}$ and $\mathrm{B}$ of a right angle triangle OAB (see figure). The resultant electric field at point $\mathrm{O}$ is perpendicular to the hypotenuse, then $\mathrm{Q}_{1} / \mathrm{Q}_{2}$ is proportional to : $\frac{x_{2}^{2}}{x_{1}^{2}}$$\frac{x_{1}^{3}}{x_{2}^{3}}$$\frac{X_{1}}{X_{2}}$$\frac{\mathrm{x}_{2}}{\mathrm{x}_{1}}$Correct Option: , 3 Solution: $\mathrm{E}_{2}=$ electric field due to $\mathrm{Q}_{2}$ $=\f...
Read More →An electron is constrained to move along the
Question: An electron is constrained to move along the y-axis with a speed of $0.1 \mathrm{c}$ ( $\mathrm{c}$ is the speed of light) in the presence of electromagnetic wave, whose electric field is $\overrightarrow{\mathrm{E}}=30 \hat{\mathrm{j}} \sin \left(1.5 \times 10^{7} \mathrm{t}-5 \times 10^{-2} \mathrm{x}\right) \mathrm{V} / \mathrm{m}$. The maximum magnetic force experienced by the electron will be : (given $\mathrm{c}=3 \times 10^{8} \mathrm{~ms}^{-1}$ and electron charge $=1.6 \times ...
Read More →The value of the acceleration due to gravity is
Question: The value of the acceleration due to gravity is $\mathrm{g}_{1}$ at a height $\mathrm{h}=\frac{\mathrm{R}}{2}(\mathrm{R}=$ radius of the earth $)$ from the surface of the earth. It is again equal to $\mathrm{g}_{1}$ at a depth $\mathrm{d}$ below the surface of the earth. The ratio $\left(\frac{\mathrm{d}}{\mathrm{R}}\right)$ equals :$\frac{7}{9}$$\frac{4}{9}$$\frac{1}{3}$$\frac{5}{9}$Correct Option: 4 Solution: $g_{2}=\frac{\operatorname{GM}(\mathrm{R}-\mathrm{d})}{\mathrm{R}^{3}}$..(2...
Read More →A wheel is rotaing freely with an angular speed
Question: A wheel is rotaing freely with an angular speed $\omega$ on a shaft. The moment of inertia of the wheel is I and the moment of inertia of the shaft is negligible. Another wheel of momet of inertia 3I initially at rest is suddenly coupled to the same shaft. The resultant fractional loss in the kinetic energy of the system is :0$\frac{1}{4}$$\frac{3}{4}$$\frac{5}{6}$Correct Option: , 3 Solution: By anglar momentum conservation $\omega I+3 I \times 0=4 I \omega^{\prime} \Rightarrow \omega...
Read More →A galvanometer of resistance
Question: A galvanometer of resistance $G$ is converted into a voltmeter of range $0-1 \mathrm{~V}$ by connecting a resistance $R_{1}$ in series with it. The additional resistance that should be connected in series with $R_{1}$ to increase the range of the voltmeter to $0-2 \mathrm{~V}$ will be :$\mathrm{R}_{1}$$\mathrm{R}_{1}+\mathrm{G}$$\mathrm{R}_{1}-\mathrm{G}$$\mathrm{G}$Correct Option: , 2 Solution: $\Rightarrow 1=\mathrm{i}_{\mathrm{g}}\left(\mathrm{G}+\mathrm{R}_{1}\right)$....(1) $\Righ...
Read More →Solve this following
Question: In the line spectra of hydrogen atom, difference between the largest and the shortest wavelengths of the Lyman series is $304 \AA$. The corresponding difference for the Paschan series in $A$ is : Solution: $\lambda=\frac{\mathrm{c}}{\left(\frac{1}{\mathrm{n}_{1}^{2}}-\frac{1}{\mathrm{n}_{2}^{2}}\right)}$ for lyman series $\lambda_{1}=\frac{\mathrm{c}}{\frac{1}{1^{2}}-\frac{1}{\infty^{2}}}=\mathrm{c}(\mathrm{n}=\infty$ to $\mathrm{n}=1)$ $\lambda_{2}=\frac{\mathrm{c}}{\frac{1}{1^{2}}-\f...
Read More →For the given input voltage waveform
Question: For the given input voltage waveform $V_{\text {in }}(t)$, the output voltage waveform $\mathrm{V}_{\mathrm{D}}(\mathrm{t})$, across the capacitor is correctly depicted by: Correct Option: 1 Solution: $\mathrm{V}_{0}(\mathrm{t})=\mathrm{V}_{\text {in }}\left(1-\mathrm{e}^{-\frac{t}{R C}}\right)$ at $\mathrm{t}=5 \mu \mathrm{s}$ $\mathrm{V}_{0}(\mathrm{t})=5\left(1-\mathrm{e}^{\frac{5 \times 10^{-6}}{10^{3} \times 10 \times 10^{-9}}}\right)$ $=5\left(1-\mathrm{e}^{-0.5}\right)=2 \mathrm...
Read More →A physical quantity
Question: A physical quantity $z$ depends on four observables a, b, c and d, as $z=\frac{a^{2} b^{\frac{2}{3}}}{\sqrt{c} d^{3}}$. The percentage of error in the measurement of $\mathrm{a}, \mathrm{b}, \mathrm{c}$ and $\mathrm{d} 2 \%, 1.5 \%, 4 \%$ and $2.5 \%$ respectively. The percentage of error in $\mathrm{z}$ is:$12.25 \%$$14.5 \%$$16.5 \%$$13.5 \%$Correct Option: , 2 Solution: $\frac{\Delta \mathrm{Z}}{\mathrm{Z}}=\frac{2 \Delta \mathrm{a}}{\mathrm{a}}+\frac{2}{3} \frac{\Delta \mathrm{b}}{...
Read More →Solve this following
Question: A closed vessel contains $0.1$ mole of a monoatomic ideal gas at $200 \mathrm{~K}$. If $0.05$ mole of the same gas at $400 \mathrm{~K}$ is added to it, the final equilibrium temperature (in $\mathrm{K}$ ) of the gas in the vessel will be closed to Solution: As work done on gas and heat supplied to the gas are zero, total internal energy of gases remain same $\mathrm{u}_{1}+\mathrm{u}_{2}=\mathrm{u}_{1}^{\prime}+\mathrm{u}_{2}^{\prime}$ $(0.1) \mathrm{C}_{\mathrm{v}}(200)+(0.05) \mathrm...
Read More →Solve this following
Question: A circular disc of mass $M$ and radius $R$ is rotating about its axis with angular speed $\omega_{1}$. If another stationary disc having radius $\frac{\mathrm{R}}{2}$ and same mass $\mathrm{M}$ is dropped co-axially on to the rotating disc. Gradually both discs attain constant angular speed $\omega_{2}$. The energy lost in the process is $\mathrm{p} \%$ of the initial energy. Value of $p$ is Solution: Let moment of inertia of bigger disc is $\mathrm{I}=\frac{\mathrm{MR}^{2}}{2}$ $\Righ...
Read More →A square loop of side
Question: A square loop of side $2 \mathrm{a}$, and carrying current $\mathrm{I}$, is kept in $\mathrm{XZ}$ plane with its centre at origin. A long wire carrying the same current I is placed parallel to the z-axis and passing through the point $(0, b, 0),(ba)$. The magnitude of the torque on the loop about zaxis is given by:$\frac{2 \mu_{0} \mathrm{I}^{2} \mathrm{a}^{2}}{\pi \mathrm{b}}$$\frac{\mu_{0} \mathrm{I}^{2} \mathrm{a}^{3}}{2 \pi \mathrm{b}^{2}}$$\frac{\mu_{0} I^{2} a^{2}}{2 \pi b}$$\fra...
Read More →Number of molecules in a volume of
Question: Number of molecules in a volume of $4 \mathrm{~cm}^{3}$ of a perfect monoatomic gas at some temperature $\mathrm{T}$ and at a pressure of $2 \mathrm{~cm}$ of mercury is close to ? (Given, mean kinetic energy of a molecule (at T) is $4 \times 10^{-14} \mathrm{erg}, \mathrm{g}=980 \mathrm{~cm} / \mathrm{s}^{2}$, density of mercury $=13.6 \mathrm{~g} / \mathrm{cm}^{3}$ )$5.8 \times 10^{18}$$5.8 \times 10^{16}$$4.0 \times 10^{18}$$4.0 \times 10^{16}$Correct Option: , 3 Solution: $\mathrm{n...
Read More →Solve this following
Question: $\mathrm{ABC}$ is a plane lamina of the shape of an equilateral triagnle. $\mathrm{D}, \mathrm{E}$ are mid points of $\mathrm{AB}$, $\mathrm{AC}$ and $\mathrm{G}$ is the centroid of the lamina. Moment of inertia of the lamina about an axis passing through $\mathrm{G}$ and perpendicular to the plane $\mathrm{ABC}$ is $\mathrm{I}_{0}$. If part ADE is removed, the moment of inertia of the remaining part about the same axis is $\frac{\mathrm{NI}_{0}}{16}$ where $\mathrm{N}$ is an integer. ...
Read More →A bullet of mass
Question: A bullet of mass $5 \mathrm{~g}$, travelling with a speed of 210 $\mathrm{m} / \mathrm{s}$, strikes a fixed wooden target. One half of its kinetic energy is converted into heat in the bullet while the other half is converted into heat in the wood. The rise of temperature of the bullet if the specific heat of its material is $0.030 \mathrm{cal} /\left(\mathrm{g}-{ }^{\circ} \mathrm{C}\right)$ ( $1 \mathrm{cal}=4.2 \times 10^{7} \mathrm{ergs}$ ) close to :$83.3^{\circ} \mathrm{C}$$87.5^{...
Read More →Assume that the displacement(s) of air is proportional to the pressure difference
Question: Assume that the displacement(s) of air is proportional to the pressure difference $(\Delta \mathrm{p})$ created by a sound wave. Displacement(s) further depends on the speed of sound (v), density of air ( $\rho$ ) and the frequency (f). If $\Delta \mathrm{p} \sim 10 \mathrm{~Pa}, \mathrm{v} \sim 300 \mathrm{~m} / \mathrm{s}, \mathrm{p} \sim 1 \mathrm{~kg} / \mathrm{m}^{3}$ and f $1000 \mathrm{~Hz}$, then $\mathrm{s}$ will be the order of (take multiplicative constant to be 1 )$10 \math...
Read More →A satellite is in an elliptical orbit around a planet P.
Question: A satellite is in an elliptical orbit around a planet P. It is observed that the velocity of the satellite when it is farthest from the planet is 6 times less than that when it is closest to the planet. The ratio of distances between the satellite and the planet at closest and farthest points is :$1: 6$$3: 4$$1: 3$$1: 2$Correct Option: 1, Solution: By angular momentum conservation $\mathrm{r}_{\min } \mathrm{v}_{\max }=\mathrm{r}_{\max } \mathrm{v}_{\min }$.......(1) Given $\mathrm{V}_...
Read More →An electrical power line, having a total resistance
Question: An electrical power line, having a total resistance of $2 \Omega$, delivers $1 \mathrm{~kW}$ at $220 \mathrm{~V}$. The efficiency of the transmission line is approximately:$72 \%$$96 \%$$91 \%$$85 \%$Correct Option: , 2 Solution: $\mathrm{vi}=10^{3}$ $\mathrm{i}=\frac{1000}{220}$ loss $=\mathrm{i}^{2} \mathrm{R}=\left(\frac{50}{11}\right)^{2} \times 2$ efficiency $=\frac{1000}{1000+\mathrm{i}^{2} \mathrm{R}} \times 100=96 \%$...
Read More →For a concave lens of focal length
Question: For a concave lens of focal length $\mathrm{f}$, the relation between object and image distance $u$ and $v$, respectively, from its pole can best be represented by ( $u=v$ is the reference line):Correct Option: 4, Solution: $v=\frac{u f}{u+f}$ Case-I If $\quad \mathrm{v}=\mathrm{u}$ $\Rightarrow \mathrm{f}+\mathrm{u}=\mathrm{f}$ $\Rightarrow \mathrm{u}=0$ Case-II If $u=\infty$ then $v=f$ Only option (4) satisfies this condition....
Read More →In a compound microscope, the magnified virtual image is formed at a distance of
Question: In a compound microscope, the magnified virtual image is formed at a distance of $25 \mathrm{~cm}$ from the eye-piece. The focal length of its objective lens is $1 \mathrm{~cm}$. If the magnification is 100 and the tube length of the microscope is $20 \mathrm{~cm}$, then the focal length of the eye-piece lens (in $\mathrm{cm}$ ) is Solution: for first lens $=\frac{1}{v_{1}}-\frac{1}{-x}=\frac{1}{1} \Rightarrow v_{1}=\frac{x}{x-1}$ also magnification $\left|\mathrm{m}_{1}\right|=\left|\...
Read More →With increasing biasing voltage of a photodiode,
Question: With increasing biasing voltage of a photodiode, the photocurrent magnitude :increases initially and saturates finallyincreases initially and after attaining certain value, it decreasesincreases linearlyremains constantCorrect Option: 1 Solution: I-V characteristic of a photodiode is as follows: On increasing the potential difference the current first increases and then attains a saturation....
Read More →A solid sphere of radius $R$ carries a charge
Question: A solid sphere of radius $R$ carries a charge $(\mathrm{Q}+\mathrm{q})$ distributed uniformly over its volume. A very small point like piece of it of mass $m$ gets detached from the bottom of the sphere and falls down vertically under gravity. This piece carries charge $\mathrm{q}$. If it acquires a speed $\mathrm{v}$ when it has fallen through a vertical height y (see figure), then : (assume the remaining portion to be spherical). $\mathrm{v}^{2}=2 \mathrm{y}\left[\frac{\mathrm{qQ}}{4...
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