The diameter of a spherical bob is measured using a vernier callipers. 9 divisions of the main scale,
Question: The diameter of a spherical bob is measured using a vernier callipers. 9 divisions of the main scale, in the vernier callipers, are equal to 10 divisions of vernier scale. One main scale division is $1 \mathrm{~mm}$. The main scale reading is $10 \mathrm{~mm}$ and $8^{\text {th }}$ division of vernier scale was found to coincide exactly with one of the main scale division. If the given vernier callipers has positive zero error of $0.04 \mathrm{~cm}$, then the radius of the bob is $\tim...
Read More →A bob of mass ' m ' suspended by a thread
Question: A bob of mass ' $m$ ' suspended by a thread of length $l$ undergoes simple harmonic oscillations with time period T. If the bob is immersed in a liquid that has density $\frac{1}{4}$ times that of the bob and the length of the thread is increased by $1 / 3^{\text {rd }}$ of the original length, then the time period of the simple harmonic oscillations will be :-$\mathrm{T}$$\frac{3}{2} \mathrm{~T}$$\frac{3}{4} T$$\frac{4}{3} T$Correct Option: , 4 Solution: $\mathrm{T}=2 \pi \sqrt{\ell /...
Read More →If velocity
Question: If velocity $[\mathrm{V}]$, time $[\mathrm{T}]$ and force $[\mathrm{F}]$ are chosen as the base quantities, the dimensions of the mass will he.$\left[\mathrm{FT}^{-1} \mathrm{~V}^{-1}\right]$$\left[\mathrm{FTV}^{-1}\right]$$\left[\mathrm{FT}^{2} \mathrm{~V}\right]$$\left[\mathrm{FVT}^{-1}\right]$Correct Option: , 2 Solution: ${[\mathrm{M}]=\mathrm{K}[\mathrm{F}]^{\mathrm{a}}[\mathrm{T}]^{\mathrm{b}}[\mathrm{V}]^{\mathrm{c}} }$ ${\left[\mathrm{M}^{\mathrm{l}}\right]=\left[\mathrm{M}^{\m...
Read More →At very high frequencies, the effective impendance
Question: At very high frequencies, the effective impendance of the given circuit will be $\Omega .$ Solution: $\mathrm{X}_{\mathrm{L}}=2 \pi \mathrm{fL}$ $\mathrm{f}$ is very large $\therefore \mathrm{X}_{\mathrm{L}}$ is very large hence open circuit. $X_{C}=\frac{1}{2 \pi f C}$ $\mathrm{f}$ is very large. $\therefore \mathrm{X}_{\mathrm{C}}$ is very small, hence short circuit. Final circuit $Z_{\mathrm{cq}}=1+\frac{2 \times 2}{2+2}=2$...
Read More →Consider two separate ideal gases of electrons
Question: Consider two separate ideal gases of electrons and protons having same number of particles. The temperature of both the gases are same. The ratio of the uncertainty in determining the position of an electron to that of a proton is proportional to :-$\left(\frac{m_{p}}{m_{e}}\right)^{3 / 2}$$\sqrt{\frac{m_{e}}{m_{p}}}$$\sqrt{\frac{m_{p}}{m_{e}}}$$\frac{m_{p}}{m_{e}}$Correct Option: , 3 Solution: $\Delta x . \Delta p \geq \frac{h}{4 \pi}$ $\Delta x=\frac{h}{4 \pi m \Delta v} \quad v=\sqr...
Read More →In a Young's double slit experiment, the slits are separated by 0.3 mm and the screen is 1.5 m away from the plane of slits
Question: In a Young's double slit experiment, the slits are separated by $0.3 \mathrm{~mm}$ and the screen is $1.5 \mathrm{~m}$ away from the plane of slits. Distance between fourth bright fringes on both sides of central bright is $2.4 \mathrm{~cm}$. The frequency of light used is__________ $\times 10^{14} \mathrm{~Hz}$ Solution: $8 \beta=2.4 \mathrm{~cm}$ $\frac{8 \lambda \Delta}{\mathrm{d}}=2.4 \mathrm{~cm}$ $\frac{8 \times 1.5 \times c}{0.3 \times 10^{-3} \times f}=2.4 \times 10^{-2}$ $f=5 ...
Read More →Solve this
Question: If $R_{E}$ be the radius of Earth, then the ratio between the acceleration due to gravity at a depth ' $r$ ' below and a height ' $r$ ' above the earth surface is : (Given : $rR_{E}$ )$1-\frac{r}{R_{E}}-\frac{r^{2}}{R_{E}^{2}}-\frac{r^{3}}{R_{E}^{3}}$$1+\frac{r}{R_{E}}+\frac{r^{2}}{R_{E}^{2}}+\frac{r^{3}}{R_{E}^{3}}$ $1+\frac{r}{R_{E}}-\frac{r^{2}}{R_{E}^{2}}+\frac{r^{3}}{R_{E}^{3}}$$1+\frac{r}{R_{E}}-\frac{r^{2}}{R_{E}^{2}}-\frac{r^{3}}{R_{E}^{3}}$Correct Option: , 4 Solution: $g_{\te...
Read More →If Va and Vb are the input voltages
Question: If $\mathrm{V}_{\mathrm{A}}$ and $\mathrm{V}_{\mathrm{B}}$ are the input voltages (either $5 \mathrm{~V}$ or $0 \mathrm{~V}$ ) and $\mathrm{V}_{\mathrm{o}}$ is the output voltage then the two gates represented in the following circuit (A) and (B) are:- AND and OR GateOR and NOT GateNAND and NOR GateAND and NOT GateCorrect Option: , 2 Solution: If $\mathrm{A}=\mathrm{B}=0$, there is no potential anywhere here $\mathrm{V}_{0}=0$ If $A=1, B=0$, Diode $D_{1}$ is forward biased, here $\math...
Read More →A particle is moving with constant acceleration ' a'.
Question: A particle is moving with constant acceleration ' $a$ '. Following graph shows $v^{2}$ versus $x$ (displacement) plot. The acceleration of the particle is______ $\mathrm{m} / \mathrm{s}^{2} .$ Solution: $y=m x+C$ $v^{2}=\frac{20}{10} x+20$ $v^{2}=2 x+20$ $2 v \frac{d v}{d x}=2$ $\therefore a=v \frac{d v}{d x}=1$...
Read More →Statement-I :
Question: Statement-I : To get a steady dc output from the pulsating voltage received from a full wave rectifier we can connect a capacitor across the output parallel to the $\operatorname{load} R_{L}$. Statement-II : To get a steady dc output from the pulsating voltage received from a full wave rectifier we can connect an inductor in series with $\mathrm{R}_{\mathrm{L}}$. In the light of the above statements, choose the most appropriate answer from the options given below:Statement I is true bu...
Read More →Solve this following
Question: A sample of gas with $\gamma=1.5$ is taken through an adiabatic process in which the volume is compressed from $1200 \mathrm{~cm}^{3}$ to $300 \mathrm{~cm}^{3}$. If the initial pressure is $200 \mathrm{kPa}$. The absolute value of the workdone by the gas in the process $=$ Solution: $v=1.5$ $\mathrm{p}_{1} \mathrm{v}_{1}^{\mathrm{v}}=\mathrm{p}_{2} \mathrm{v}_{2}^{\mathrm{v}}$ $(200)(1200)^{1.5}=\mathrm{P}^{2}(300)^{1.5}$ $\mathrm{P}_{2}=200[4]^{3 / 2}=1600 \mathrm{kPa}$ $\mid$ W.D. $\...
Read More →For a body executing S.H.M. :
Question: For a body executing S.H.M. : (a) Potential energy is always equal to its K.E. (b) Average potential and kinetic energy over any given time interval are always equal. (c) Sum of the kinetic and potential energy at any point of time is constant. (d) Average K.E. in one time period is equal to average potential energy in one time period. Choose the most appropriate option from the options given below :(c) and (d)only (c)(b) and (c)only (b)Correct Option: 1 Solution: In S.H.M. total mecha...
Read More →A long solenoid with 1000 turns/m has a core material with relative permeability 500 and volume
Question: A long solenoid with 1000 turns $/ \mathrm{m}$ has a core material with relative permeability 500 and volume $10^{3} \mathrm{~cm}^{3}$. If the core material is replaced by another material having relative permeability of 750 with same volume maintaining same current of $0.75 \mathrm{~A}$ in the solenoid, the fractional change in the magnetic moment of the core would be approximately $\left(\frac{x}{499}\right)$. Find the value of $x$. Solution: $\frac{\Delta \mathrm{M}}{\mathrm{M}}=\fr...
Read More →A coil is placed in a magnetic
Question: A coil is placed in a magnetic field $\overrightarrow{\mathrm{B}}$ as shown below: A current is induced in the coil because $\overrightarrow{\mathrm{B}}$ is :Outward and decreasing with timeParallel to the plane of coil and decreasing with timeOutward and increasing with timeParallel to the plane of coil and increasing with timeCorrect Option: 1 Solution: $\overrightarrow{\mathrm{B}}$ must not be parallel to the plane of coil for non zero flux and according to lenz law if B is outward ...
Read More →Two thin metallic spherical shells of radii
Question: Two thin metallic spherical shells of radii $r_{1}$ and $r_{2}$ $\left(r_{1}r_{2}\right)$ are placed with their centres coinciding. A material of thermal conductivity $\mathrm{K}$ is filled in the space between the shells. The inner shell is maintained at temperature $\theta_{1}$ and the outer shell at temperature $\theta_{2}\left(\theta_{1}\theta_{2}\right)$. The rate at which heat flows radially through the material is :-$\frac{4 \pi \mathrm{Kr}_{1} \mathrm{r}_{2}\left(\theta_{2}-\th...
Read More →A block moving horizontally
Question: A block moving horizontally on a smooth surface with a speed of $40 \mathrm{~m} / \mathrm{s}$ splits into two parts with masses in the ratio of $1: 2$. If the smaller part moves at $60 \mathrm{~m} / \mathrm{s}$ in the same direction, then the fractional change in kinetic energy is :-$\frac{1}{3}$$\frac{2}{3}$$\frac{1}{8}$$\frac{1}{4}$Correct Option: , 3 Solution: $3 \mathrm{MV}_{0}=2 \mathrm{MV}_{2}+\mathrm{MV}_{1}$ $3 \mathrm{~V}_{0}=2 \mathrm{~V}_{2}+\mathrm{V}_{1}$ $120=2 \mathrm{~V...
Read More →A parallel plate capacitor of capacitance 200 µF is connected to a battery of 200 V.
Question: A parallel plate capacitor of capacitance 200 F is connected to a battery of 200 V. A dielectric slab of dielectric constant 2 is now inserted into the space between plates of capacitor while the battery remain connected. The change in the electrostatic energy in the capacitor will be_____J. Solution: $\Delta \mathrm{U}=\frac{1}{2}(\Delta \mathrm{C}) \mathrm{V}^{2}$ $\Delta \mathrm{U}=\frac{1}{2}(\mathrm{KC}-\mathrm{C}) \mathrm{V}^{2}$ $\Delta \mathrm{U}=\frac{1}{2}(2-1) \mathrm{CV}^{2...
Read More →Solve this following
Question: A resistor dissipates $192 \mathrm{~J}$ of energy in $1 \mathrm{~s}$ when a current of $4 \mathrm{~A}$ is passed through it. Now, when the current is doubled, the amount of thermal energy dissipated in $5 \mathrm{~s}$ in Solution: $\mathrm{E}=i^{2} \mathrm{Rt}$ $192=16(\mathrm{R})(1)$ $\mathrm{R}=12 \Omega$ $\mathrm{E}^{1}=(8)^{2}(12)(5)$ $=3840 \mathrm{~J}$...
Read More →A free electron of
Question: A free electron of $2.6 \mathrm{eV}$ energy collides with a $\mathrm{H}^{+}$ion. This results in the formation of a hydrogen atom in the first excited state and a photon is released. Find the frequency of the emitted photon. $\left(h=6.6 \times 10^{-34} \mathrm{Js}\right)$$1.45 \times 10^{16} \mathrm{MHz}$$0.19 \times 10^{15} \mathrm{MHz}$$1.45 \times 10^{9} \mathrm{MHz}$$9.0 \times 10^{27} \mathrm{MHz}$Correct Option: , 3 Solution: For every large distance P.E. $=0$ $\$ total energy $...
Read More →A bandwidth of 6 MHz is available for A.M. transmission.
Question: A bandwidth of 6 MHz is available for A.M. transmission. If the maximum audio signal frequency used for modulating the carrier wave is not to exceed 6 kHz. The number of stations that can be broadcasted within this band simultaneously without interfering with each other will be______. Solution: Signal bandwidth $=2 \mathrm{fm}$ $=12 \mathrm{kHz}$ $\therefore \mathrm{N}=\frac{6 \mathrm{MHZ}}{12 \mathrm{kHZ}}=\frac{6 \times 10^{6}}{12 \times 10^{3}}=500$...
Read More →A mixture of hydrogen
Question: A mixture of hydrogen and oxygen has volume $500 \mathrm{~cm}^{3}$, temperature $300 \mathrm{~K}$, pressure $400 \mathrm{kPa}$ and mass $0.76 \mathrm{~g}$. The ratio of masses of oxygen to hydrogen will be :-$3: 8$$3: 16$$16: 3$$8: 3$Correct Option: , 3 Solution: $P V=n R T$ $400 \times 10^{3} \times 500 \times 10^{-6}=n\left(\frac{25}{3}\right)(300)$ $\mathrm{n}=\frac{2}{25}$ $\mathrm{n}=\mathrm{n}_{1}+\mathrm{n}_{2}$ $\frac{2}{25}=\frac{\mathrm{M}_{1}}{2}+\frac{\mathrm{M}_{2}}{32}$ A...
Read More →Cross-section view of a prism is the equilateral triangle
Question: Cross-section view of a prism is the equilateral triangle $\mathrm{ABC}$ in the figure. The minimum deviation is observed using this prism when the angle of incidence is equal to the prism angle. The time taken by light to travel from $\mathrm{P}$ (midpoint of $\mathrm{BC}$ ) to $\mathrm{A}$ is $\times 10^{-10} \mathrm{~s}$. (Given, speed of light in vacuum $=3 \times 10^{8} \mathrm{~m} / \mathrm{s}$ and $\left.\cos 30^{\circ}=\frac{\sqrt{3}}{2}\right)$ Solution: $\mathrm{i}=\mathrm{A}...
Read More →Statement I : Two forces
Question: Statement I : Two forces $(\overrightarrow{\mathrm{P}}+\overrightarrow{\mathrm{Q}})$ and $(\overrightarrow{\mathrm{P}}-\overrightarrow{\mathrm{Q}})$ where $\overrightarrow{\mathrm{P}} \perp \overrightarrow{\mathrm{Q}}$, when act at an angle $\theta_{1}$ to each other, the magnitude of their resultant is $\sqrt{3\left(\mathrm{P}^{2}+\mathrm{Q}^{2}\right)}$, when they act at an angle $\theta_{2}$, the magnitude of their resultant becomes $\sqrt{2\left(\mathrm{P}^{2}+\mathrm{Q}^{2}\right)...
Read More →Choose the incorrect statement:
Question: Choose the incorrect statement: (a) The electric lines of force entering into a Gaussian surface provide negative flux. (b) A charge ' $q$ ' is placed at the centre of a cube. The flux through all the faces will be the same. (c) In a uniform electric field net flux through a closed Gaussian surface containing no net charge, is zero. (d) When electric field is parallel to a Gaussian surface, it provides a finite non-zero flux. Choose the most appropriate answer from the options given be...
Read More →A system consists of two identical spheres each of mass
Question: A system consists of two identical spheres each of mass $1.5 \mathrm{~kg}$ and radius $50 \mathrm{~cm}$ at the end of light rod. The distance between the centres of the two spheres is $5 \mathrm{~m}$. What will be the moment of inertia of the system about an axis perpendicular to the rod passing through its midpoint?$18.75 \mathrm{kgm}^{2}$$1.905 \times 10^{5} \mathrm{kgm}^{2}$$19.05 \mathrm{kgm}^{2}$$1.875 \times 10^{5} \mathrm{kgm}^{2}$Correct Option: , 3 Solution: $\mathrm{M}=1.5 \m...
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