Consider a badminton racket with length scales as shown in the figure.
Question: Consider a badminton racket with length scales as shown in the figure. If the mass of the linear and circular portions of the badminton racket are same (M) and the mass of the threads are negligible, the moment of inertia of the racket about an axis perpendicular to the handle and in the plane of the ring at, $\frac{r}{2}$ distance from the end $\mathrm{A}$ of the handle will be ........ $\mathrm{Mr}^{2}$. Solution: $I=\left[I_{1}+M\left(\frac{5}{2} r\right)^{2}\right]+\left[I_{2}+M\le...
Read More →Two identical antennas mounted on identical towers are separated from each other by
Question: Two identical antennas mounted on identical towers are separated from each other by a distance of $45 \mathrm{~km}$. What should nearly be the minimum height of receiving antenna to receive the signals in line of sight? (Assume radius of earth is $6400 \mathrm{~km}$ ) (Assume radius of earth is $6400 \mathrm{~km}$ )$19.77 \mathrm{~m}$$39.55 \mathrm{~m}$$79.1 \mathrm{~m}$$158.2 \mathrm{~m}$Correct Option: , 2 Solution: $\mathrm{D}=2 \sqrt{2 \mathrm{Rh}}$ $h=\frac{\mathrm{D}^{2}}{8 \math...
Read More →Two cars X and Y
Question: Two cars $\mathrm{X}$ and $\mathrm{Y}$ are approaching each other with velocities $36 \mathrm{~km} / \mathrm{h}$ and $72 \mathrm{~km} / \mathrm{h}$ respectively. The frequency of a whistle sound as emitted by a passenger in car X, heard by the passenger in car $\mathrm{Y}$ is $1320 \mathrm{~Hz}$. If the velocity of sound in air is $340 \mathrm{~m} / \mathrm{s}$, the actual frequency of the whistle sound produced is ........ Hz. Solution: $\mathrm{V}_{\mathrm{x}}=36 \mathrm{~km} / \math...
Read More →The speed of electrons in a scanning electron microscope
Question: The speed of electrons in a scanning electron microscope is $1 \times 10^{7} \mathrm{~ms}^{-1}$. If the protons having the same speed are used instead of electrons, then the resolving power of scanning proton microscope will be changed by a factor of:1837$\frac{1}{1837}$$\sqrt{1837}$$\frac{1}{\sqrt{1837}}$Correct Option: 1 Solution: Resolving power $(\mathrm{RP}) \propto \frac{1}{\lambda}$ $\lambda=\frac{\mathrm{h}}{\mathrm{P}}=\frac{\mathrm{h}}{\mathrm{mv}}$ So $(\mathrm{RP}) \propto ...
Read More →White light is passed through a double slit and interference is observed on a screen
Question: White light is passed through a double slit and interference is observed on a screen $1.5 \mathrm{~m}$ away. The separation between the slits is $0.3 \mathrm{~mm}$. The first violet and red fringes are formed $2.0 \mathrm{~mm}$ and $3.5 \mathrm{~mm}$ away from the central white fringes. The difference in wavelengths of red and voilet light is $\mathrm{nm}$. Solution: Position of bright fringe $\mathrm{y}=\mathrm{n} \frac{\mathrm{D} \lambda}{\mathrm{d}}$ $\mathrm{y}_{1}$ of red $=\frac{...
Read More →First, a set of
Question: First, a set of $\mathrm{n}$ equal resistors of $10 \Omega$ each are connected in series to a battery of emf $20 \mathrm{~V}$ and internal resistance $10 \Omega$. A current $\mathrm{I}$ is observed to flow. Then, the $n$ resistors are connected in parallel to the same battery. It is observed that the current is increased 20 times, then the value of $n$ is Solution: In series $\mathrm{R}_{\mathrm{eq}}=\mathrm{nR}=10 \mathrm{n}$ $\mathrm{i}_{\mathrm{s}}=\frac{20}{10+10 \mathrm{n}}=\frac{...
Read More →Statement I : A cyclist is moving on an
Question: Statement I : A cyclist is moving on an unbanked road with a speed of $7 \mathrm{kmh}^{-1}$ and takes a sharp circular turn along a path of radius of $2 \mathrm{~m}$ without reducing the speed. The static friction coefficient is $0.2$. The cyclist will not slip and pass the curve $\left(\mathrm{g}=9.8 \mathrm{~m} / \mathrm{s}^{2}\right)$ In the light of the above statements, choose the correct answer from the options given below. Statement II : If the road is banked at an angle of $45^...
Read More →Considew a sample of oxygen behaving like an ideal gas.
Question: Considew a sample of oxygen behaving like an ideal gas. At $300 \mathrm{~K}$, the ratio of root mean square (rms) velocity to the average velocity of gas molecule would be : (Molecular weight of oxygen is $32 \mathrm{~g} / \mathrm{mol}$; $R=8.3 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$ ) $\sqrt{\frac{3}{3}}$$\sqrt{\frac{8}{3}}$$\sqrt{\frac{3 \pi}{8}}$$\sqrt{\frac{8 \pi}{3}}$Correct Option: , 3 Solution: $\mathrm{v}_{\mathrm{rms}}=\sqrt{\frac{3 R T}{M}}$ $\mathrm{v}_{\mathrm{avg}...
Read More →A circuit is arranged
Question: A circuit is arranged as shown in figure. The output voltage $V_{0}$ is equal to ....... V. Solution: As diodes $D_{1}$ and $D_{2}$ are in forward bias, so they acted as neligible resistances $\Rightarrow$ Input voltage become zero $\Rightarrow$ Input current is zero $\Rightarrow$ Output current is zero $\Rightarrow \mathrm{V}_{0}=5$ volt...
Read More →Two travelling waves produces a standing wave represented by equation,
Question: Two travelling waves produces a standing wave represented by equation, $\mathrm{y}=1.0 \mathrm{~mm} \cos \left(1.57 \mathrm{~cm}^{-1}\right) \mathrm{x} \sin \left(78.5 \mathrm{~s}^{-1}\right) \mathrm{t}$ The node closest to the origin in the region $x0$ will be at $x=$ $\mathrm{cm}$. Solution: For node $\cos \left(1.57 \mathrm{~cm}^{-1}\right) \mathrm{x}=0$ $\left(1.57 \mathrm{~cm}^{-1}\right) \mathrm{x}=\frac{\pi}{2}$ $x=\frac{\pi}{2(1.57)} \mathrm{cm}=1 \mathrm{~cm}$ Ans. $1.00$...
Read More →A uniform conducting
Question: A uniform conducting wire of length is $24 \mathrm{a}$, and resistance $R$ is wound up as a current carrying coil in the shape of an equilateral triangle of side 'a' and then in the form of a square of side 'a'. The coil is connected to a voltage source $\mathrm{V}_{0}$. The ratio of magnetic moment of the coils in case of equilateral triangle to that for square is $1: \sqrt{\mathrm{y}}$ where $\mathrm{y}$ is Solution: In triangle shape $\mathrm{N}_{\mathrm{t}}=\frac{24 \mathrm{a}}{3 \...
Read More →An ideal gas in a cylinder is separated by
Question: An ideal gas in a cylinder is separated by a piston in such a way that the entropy of one part is $S_{1}$ and that of the other part is $S_{2}$. Given that $\mathrm{S}_{1}\mathrm{S}_{2}$. If the piston is removed then the total entropy of the system will be :$S_{1} \times S_{2}$$S_{1}-S_{2}$$\frac{S_{1}}{S_{2}}$$S_{1}+S_{2}$Correct Option: , 4 Solution:...
Read More →A particle of mass m moves in a circular orbit
Question: A particle of mass $m$ moves in a circular orbit under the central potential field, $U(\mathrm{r})=\frac{-\mathrm{C}}{\mathrm{r}}$, where $\mathrm{C}$ is a positive constant. The correct radius - velocity graph of the particle's motion is : Correct Option: Solution: $\mathrm{U}=-\frac{\mathrm{C}}{\mathrm{r}}$ $\mathrm{F}=-\frac{\mathrm{dU}}{\mathrm{dr}}=-\frac{\mathrm{C}}{\mathrm{r}^{2}}$ $|\mathrm{F}|=\frac{m v^{2}}{r}$ $\frac{\mathrm{C}}{\mathrm{r}^{2}}=\frac{\mathrm{mv}^{2}}{\mathrm...
Read More →Two short magnetic dipoles
Question: Two short magnetic dipoles $\mathrm{m}_{1}$ and $\mathrm{m}_{2}$ each having magnetic moment of $1 \mathrm{Am}^{2}$ are placed at point $\mathrm{O}$ and $P$ respectively. The distance between OP is 1 meter. The torque experienced by the magnetic dipole $\mathrm{m}_{2}$ due to the presence of $\mathrm{m}_{1}$ is ...... $\times 10^{-7} \mathrm{Nm}$. Solution: $\vec{\tau}=\overrightarrow{\mathrm{M}}_{2} \times \overrightarrow{\mathrm{B}}_{1}$ $\tau=\mathrm{M}_{2} \mathrm{~B}_{1} \sin 90^{...
Read More →The alternating current
Question: The alternating current is given by $i=\left\{\sqrt{42} \sin \left(\frac{2 \pi}{T} t\right)+10\right\} A$ The r.m.s. value of this current is A. Solution: $f_{\mathrm{rms}}^{2}=\mathrm{f}_{1 \mathrm{rms}}^{2}+\mathrm{f}_{2 \mathrm{rms}}^{2}$ $=\left(\frac{\sqrt{42}}{\sqrt{2}}\right)^{2}+10^{2}$ $=121 \Rightarrow \mathrm{f}_{\mathrm{ms}}=11 \mathrm{~A}$...
Read More →A body of mass
Question: A body of mass (2M) splits into four masses $\{\mathrm{m}, \mathrm{M}-\mathrm{m}, \mathrm{m}, \mathrm{M}-\mathrm{m}\}$, which are rearranged to form a square as shown in the figure. The ratio of $\frac{\mathrm{M}}{\mathrm{m}}$ for which, the gravitational potential energy of the system becomes maximum is $x: 1$. The value of $x$ is ....... Solution: Energy is maximum when mass is split equally so $\frac{M}{m}=2$...
Read More →A resistor develops 500J of thermal energy in 20 s when a current of 1.5 A is passed through it.
Question: A resistor develops $500 \mathrm{~J}$ of thermal energy in $20 \mathrm{~s}$ when a current of $1.5 \mathrm{~A}$ is passed through it. If the current is increased from $1.5 \mathrm{~A}$ to $3 \mathrm{~A}$, what will be the energy developed in $20 \mathrm{~s}$.$1500 \mathrm{~J}$$1000 \mathrm{~J}$$500 \mathrm{~J}$$2000 \mathrm{~J}$Correct Option: , 4 Solution: $500=(1.5)^{2} \times \mathrm{R} \times 20$ $\mathrm{E}=(3)^{2} \times \mathrm{R} \times 20$ $\mathrm{E}=2000 \mathrm{~J}$...
Read More →The time taken for the magnetic energy to reach
Question: The time taken for the magnetic energy to reach $25 \%$ of its maximum value, when a solenoid of resistance $\mathrm{R}$, inductance $\mathrm{L}$ is connected to a battery, is :$\frac{L}{R} \ell n 5$infinite$\frac{L}{R} \ell \ln 2$$\frac{L}{R} \ell \operatorname{nn} 10$Correct Option: , 3 Solution: Magnetic energy $=\frac{1}{2} \mathrm{Li}^{2}=25 \%$ $\mathrm{ME} \Rightarrow 25 \% \Rightarrow \mathrm{i}=\frac{\mathrm{i}_{0}}{2}$ $\mathrm{i}=\mathrm{i}_{0}\left(1-\mathrm{R}^{-\mathrm{R}...
Read More →The variation of displacement
Question: The variation of displacement with time of a particle executing free simple harmonic motion is shown in the figure. The potential energy $U(x)$ versus time $(t)$ plot of the particle is correctly shown in figure :Correct Option: , 4 Solution: Potential energy is maximum at maximum distance from mean....
Read More →An amplitude modulated wave is represented by
Question: An amplitude modulated wave is represented by $C_{m}(t)=10(1+0.2 \cos 12560 t) \sin \left(111 \times 10^{4} t\right)$ volts. The modulating frequency in $\mathrm{kHz}$ will be Solution: $\mathrm{W}_{\mathrm{m}}=12560=2 \pi \mathrm{f}_{\mathrm{m}}$ $f_{m}=\frac{12560}{2 \pi}$ $=2000 \mathrm{~Hz}$ Ans. $2.00$...
Read More →A solid cylinder of mass m is wrapped
Question: A solid cylinder of mass $m$ is wrapped with an inextensible light string and, is placed on a rough inclined plane as shown in the figure. The frictional force acting between the cylinder and the inclined plane is : [The coefficient of static friction, $\mu_{\mathrm{s}}$, is $\left.0.4\right]$$\frac{7}{2} \mathrm{mg}$$5 \mathrm{mg}$$\frac{\mathrm{mg}}{5}$0Correct Option: , 3 Solution: Let's take solid cylinder is in equilibrium $T+f=m g \sin 60$ ...................(1) $\mathrm{TR}-\mat...
Read More →Five identical cells
Question: Five identical cells each of internal resistance $1 \Omega$ and emf $5 \mathrm{~V}$ are connected in series and in parallel with an external resistance ' $R$ '. For what value of ' $R$ ', current in series and parallel combination will remain the same ?$1 \Omega$$25 \Omega$$5 \Omega$$10 \Omega$Correct Option: 1 Solution: $\mathrm{i}_{1}=\frac{25}{5+\mathrm{R}}$ $\mathrm{i}_{2}=\frac{5}{\mathrm{R}+\frac{1}{5}}$ $\mathrm{i}_{1}=\mathrm{i}_{2} \Rightarrow 5\left(\mathrm{R}+\frac{1}{5}\rig...
Read More →A bimetallic strip consists of metals A and B. It is mounted rigidly as shown.
Question: A bimetallic strip consists of metals A and B. It is mounted rigidly as shown. The metal $\mathrm{A}$ has higher coefficient of expansion compared to that of metal B. When the bimetallic strip is placed in a cold both, it will: Bend towards the rightNot bend but shrinkNeither bend nor shrinkBend towards the leftCorrect Option: , 4 Solution: $\alpha_{A}\alpha_{B}$ Length of both strips will decrease $\Delta \mathrm{L}_{\mathrm{A}}\Delta \mathrm{L}_{\mathrm{B}}$...
Read More →The function of time representing a simple
Question: The function of time representing a simple harmonic motion with a period of $\frac{\pi}{\omega}$ is :$\sin (\omega t)+\cos (\omega t)$$\cos (\omega t)+\cos (2 \omega t)+\cos (3 \omega t)$$\sin ^{2}(\omega t)$$3 \cos \left(\frac{\pi}{4}-2 \omega t\right)$Correct Option: , 4 Solution: Time period $\mathrm{T}=\frac{2 \pi}{\omega^{\prime}}$ $\frac{\pi}{\omega}=\frac{2 \pi}{\omega^{\prime}}$ $\omega^{\prime}=2 \omega \rightarrow$ Angular frequency of SHM Option (3) $\sin ^{2} \omega \mathrm...
Read More →In order to determine the Young's Modulus of a wire of radius 0.2cm (measured using a scale of least count =0.001cm)
Question: In order to determine the Young's Modulus of a wire of radius $0.2 \mathrm{~cm}$ (measured using a scale of least count $=0.001 \mathrm{~cm}$ ) and length $1 \mathrm{~m}$ (measured using a scale of least count $=1 \mathrm{~mm}$ ), a weight of mass $1 \mathrm{~kg}$ (measured using a scale of least count $=1 \mathrm{~g}$ ) was hanged to get the elongation of $0.5 \mathrm{~cm}$ (measured using a scale of least count $0.001 \mathrm{~cm}$ ). What will be the fractional error in the value of...
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