A wire having a linear mass density
Question: A wire having a linear mass density $9.0 \times 10^{-4} \mathrm{~kg} / \mathrm{m}$ is stretched between two rigid supports with a tension of $900 \mathrm{~N}$. The wire resonates at a frequency of $500 \mathrm{~Hz}$. The next higher frequency at which the same wire resonates is $550 \mathrm{~Hz}$. The length of the wire is_________m. Solution: $\mu=9.0 \times 10^{-4} \frac{\mathrm{kg}}{\mathrm{m}}$ $T=900 \mathrm{~N}$ $\mathrm{V}=\sqrt{\frac{\mathrm{T}}{\mu}}=\sqrt{\frac{900}{9 \times ...
Read More →A glass tumbler having inner depth of 17.5cm is kept on a table.
Question: A glass tumbler having inner depth of $17.5 \mathrm{~cm}$ is kept on a table. A student starts pouring water $(\mu=4 / 3)$ into it while looking at the surface of water from the above. When he feels that the tumbler is half filled, he stops pouring water. Up to what height, the tumbler is actually filled ?11.7 cm10 cm7.5 cm8.75 cmCorrect Option: , 2 Solution: Height of water observed by observer $=\frac{H}{\mu_{w}}=\frac{H}{(4 / 3)}=\frac{3 H}{4}$ Height of air observed by observer = 1...
Read More →A square shaped wire with resistance of each
Question: A square shaped wire with resistance of each side $3 \Omega$ is bent to form a complete circle. The resistance between two diametrically opposite points of the circle in unit of $\Omega$ will be_________. Solution: $\mathrm{R}_{\mathrm{eq}}=3 \Omega$...
Read More →If the sum of the heights of transmitting and
Question: If the sum of the heights of transmitting and receiving antennas in the line of sight of communication is fixed at $160 \mathrm{~m}$, then the maximum range of LOS communication is $\mathrm{km}$. $($ Take radius of Earth $=6400 \mathrm{~km})$ Solution: $\mathrm{h}_{\mathrm{T}}=\mathrm{h}_{\mathrm{R}}=160 \ldots$ (i) $\mathrm{d}=\sqrt{2 \mathrm{Rh}_{\mathrm{T}}}+\sqrt{2 \mathrm{Rh}_{\mathrm{R}}}$ $d=\sqrt{2 R}\left[\sqrt{h_{T}}+\sqrt{h_{R}}\right]$ $d=\sqrt{2 R}[\sqrt{x}+\sqrt{160-x}]$ ...
Read More →Following plots show Magnetization (M) vs Magnetising field (H) and Magnetic susceptibility ( F ) vs temperature (T) graph :
Question: Following plots show Magnetization (M) vs Magnetising field (H) and Magnetic susceptibility ( F ) vs temperature (T) graph : Which of the following combination will be represented by a diamagnetic material?(a), (c)$(a),(d)$$(b),(d)$$(b),(c)$Correct Option: 1, Solution: Conceptual question Option (1)...
Read More →A particle of mass
Question: A particle of mass $1 \mathrm{~kg}$ is hanging from a spring of force constant $100 \mathrm{Nm}^{-1}$. The mass is pulled slightly downward and released so that it executes free simple harmonic motion with time period $\mathrm{T}$. The time when the kinetic energy and potential The time when the kinetic energy and potential energy of the system will become equal, is $\frac{T}{x}$. The value of $x$ is_______. Solution: $\mathrm{KE}=\mathrm{PE}$ $\mathrm{y}=\frac{\mathrm{A}}{\sqrt{2}}=\m...
Read More →When a rubber ball is taken to a depth
Question: When a rubber ball is taken to a depth of $m$ in deep sea, its volume decreases by $0.5 \%$ (The bulk modulus of rubber $=9.8 \times 10^{8} \mathrm{Nm}^{-2}$ Density of sea water $=10^{3} \mathrm{kgm}^{-3}$ $\left.\mathrm{g}=9.8 \mathrm{~m} / \mathrm{s}^{2}\right)$ Solution: $\mathrm{B}=-\frac{\Delta \mathrm{P}}{\left(\frac{\Delta \mathrm{V}}{\mathrm{V}}\right)}=-\frac{\rho \mathrm{gh}}{\left(\frac{\Delta \mathrm{V}}{\mathrm{V}}\right)}$ $-\frac{\mathrm{B} \frac{\Delta \mathrm{V}}{\mat...
Read More →Solve this following
Question: The coefficient of static friction between two blocks is $0.5$ and the table is smooth. The maximum horizontal force that can be applied to move the blocks together is .......N. $\left(\right.$ take $\left.\mathrm{g}=10 \mathrm{~ms}^{-2}\right)$ Solution: $\mathrm{F}=3 \mathrm{a}($ For system $)$ ........................(I) $\mathrm{fs}_{\max }=1 \mathrm{a}($ for $1 \mathrm{~kg}$ block) ..................(II) $\mu \times 1 \times g=a$ $\Rightarrow 5=\mathrm{a}$ $\mathrm{F}=15 \mathrm{~...
Read More →The half life period of radioactive element x is same as the mean life time of another radioactive element y. Initially they have the same number of atoms. Then :
Question: The half life period of radioactive element $x$ is same as the mean life time of another radioactive element y. Initially they have the same number of atoms. Then :$x$-will decay faster than $y$.$\mathrm{y}-$ will decay faster than $\mathrm{x}$.$x$ and $y$ have same decay rate initially and later on different decay rate.x and y decay at the same rate always.Correct Option: , 2 Solution: $\left(t_{1 / 2}\right)_{x}=(\tau)_{y}$ $\Rightarrow \frac{\ell \mathrm{n} 2}{\lambda_{\mathrm{x}}}=...
Read More →Consider a galvanometer shunted with
Question: Consider a galvanometer shunted with $5 \Omega$ resistance and $2 \%$ of current passes through it. What is the resistance of the given galvanometer ?$300 \Omega$$344 \Omega$$245 \Omega$$226 \Omega$Correct Option: , 3 Solution: $0.02 \mathrm{i} \mathrm{Rg}=0.98 \mathrm{i} \times 5$ $R g=245 \Omega$ Option (3)...
Read More →A moving proton and electron have the same
Question: A moving proton and electron have the same deBroglie wavelength. If $\mathrm{K}$ and $P$ denote the $\mathrm{K} . \mathrm{E}$. and momentum respectively. Then choose the correct option :$\mathrm{K}_{\mathrm{p}}\mathrm{K}_{\mathrm{e}}$ and $\mathrm{P}_{\mathrm{p}}=\mathrm{P}_{\mathrm{e}}$$\mathrm{K}_{\mathrm{p}}=\mathrm{K}_{\mathrm{e}}$ and $\mathrm{P}_{\mathrm{p}}=\mathrm{P}_{\mathrm{e}}$$\mathrm{K}_{\mathrm{p}}\mathrm{K}_{\mathrm{e}}$ and $\mathrm{P}_{\mathrm{p}}\mathrm{P}_{\mathrm{e}...
Read More →An object is placed at a distance of
Question: An object is placed at a distance of $12 \mathrm{~cm}$ from a convex lens. A convex mirror of focal length $15 \mathrm{~cm}$ is placed on other side of lens at $8 \mathrm{~cm}$ as shown in the figure. Image of object coincides with the object. When the convex mirror is removed, a real and inverted image is formed at a position. The distance of the image from the object will be . (cm) Solution: For the object to coincide with image, the light must fall perpendicularly to mirror. Which m...
Read More →solve this
Question: Two resistors $\mathrm{R}_{1}=(4 \pm 0.8) \Omega$ and $\mathrm{R}_{2}=(4 \pm 0.4)$ $\Omega$ are connected in parallel. The equivalent resistance of their parallel combination will be:$(4 \pm 0.4) \Omega$$(2 \pm 0.4) \Omega$$(2 \pm 0.3) \Omega$$(4 \pm 0.3) \Omega$Correct Option: , 3 Solution: $\frac{1}{R_{\text {cq }}}=\frac{1}{R_{1}}+\frac{1}{R_{2}}$ $\frac{1}{\mathrm{R}_{\mathrm{eq}}}=\frac{1}{4}+\frac{1}{4} \Rightarrow \mathrm{R}_{\mathrm{eq}}=2 \Omega$ Also $\frac{\Delta \mathrm{R}_...
Read More →For the given circuit, the power across zener diode is
Question: For the given circuit, the power across zener diode is .......... $\mathrm{mW}$. Solution: $\mathrm{i}=\frac{10 \mathrm{~V}}{5 \mathrm{k} \Omega}=2 \mathrm{~mA}$ $\mathrm{I}=\frac{14 \mathrm{~V}}{1 \mathrm{k} \Omega}=14 \mathrm{~mA}$ $\therefore \mathrm{I}_{\mathrm{z}}=12 \mathrm{~mA}$ $\therefore \mathrm{P}=\mathrm{I}_{\mathrm{z}} \mathrm{V}_{\mathrm{z}}=120 \mathrm{~mW}$ Ans. 120...
Read More →In an ac circuit, an inductor,
Question: In an ac circuit, an inductor, a capacitor and a resistor are connected in series with $X_{L}=R=X_{C}$. Impedance of this circuit is :$2 R^{2}$Zero$R$$R \sqrt{2}$Correct Option: , 3 Solution: $\mathrm{Z}=\sqrt{\left(\mathrm{X}_{\mathrm{L}}-\mathrm{X}_{\mathrm{C}}\right)^{2}+\mathrm{R}^{2}}=\mathrm{R} \because \mathrm{X}_{\mathrm{L}}=\mathrm{X}_{\mathrm{C}}$ Option (3)...
Read More →A student determined Young's Modulus of
Question: A student determined Young's Modulus of elasticity using the formula $\mathrm{Y}=\frac{\mathrm{MgL}^{3}}{4 \mathrm{bd}^{3} \delta}$. The value of $\mathrm{g}$ is taken to be $9.8 \mathrm{~m} / \mathrm{s}^{2}$, without any significant error, his observation are as following. Then the fractional error in the measurement of $Y$ is:$0.0083$$0.0155$$0.155$$0.083$Correct Option: , 2 Solution: $\mathrm{y}=\frac{\mathrm{MgL}^{3}}{4 \mathrm{bd}^{3} \delta}$ $\frac{\Delta \mathrm{y}}{\mathrm{y}}...
Read More →A coil in the shape of an equilateral triangle of side
Question: A coil in the shape of an equilateral triangle of side $10 \mathrm{~cm}$ lies in a vertical plane between the pole pieces of permanent magnet producing a horizontal magnetic field $20 \mathrm{mT}$. The torque acting on the coil when a current of $0.2 \mathrm{~A}$ is passed through it and its plane becomes parallel to the magnetic field will be $\sqrt{\mathrm{x}} \times 10^{-5} \mathrm{Nm}$. The value of $\mathrm{x}$ is.......... Solution: $\vec{\tau}=\overrightarrow{\mathrm{M}} \times ...
Read More →Angular momentum of a single particle moving
Question: Angular momentum of a single particle moving with constant speed along circular path :changes in magnitude but remains same in the directionremains same in magnitude and directionremains same in magnitude but changes in the directionis zeroCorrect Option: , 2 Solution: $|\overrightarrow{\mathrm{L}}|=\mathrm{mVr}$ And direction will be upward \ remain constant Option (2)...
Read More →Two simple harmonic motions are represented by the equations
Question: Two simple harmonic motions are represented by the equations $\mathrm{x}_{1}=5 \sin \left(2 \pi \mathrm{t}+\frac{\pi}{4}\right)$ and $\mathrm{x}_{2}=5 \sqrt{2}(\sin 2 \pi \mathrm{t}+\cos 2 \pi \mathrm{t})$ The amplitude of second motion is times the amplitude in first motion. Solution: $\mathrm{x}_{2}=5 \sqrt{2}\left(\frac{1}{\sqrt{2}} \sin 2 \pi \mathrm{t}+\frac{1}{\sqrt{2}} \cos 2 \pi \mathrm{t}\right) \sqrt{2}$ $=10 \sin \left(2 \pi t+\frac{\pi}{4}\right)$ $\therefore \frac{\mathrm{...
Read More →Which of the following equations is dimensionally incorrect?
Question: Which of the following equations is dimensionally incorrect? Where $\mathrm{t}=$ time, $\mathrm{h}=$ height, $\mathrm{s}=$ surface tension, $\theta=$ angle,$\rho=$ density, a, $r=$ radius, $\mathrm{g}=$ acceleration due to gravity, $\mathrm{v}=$ volume, $\mathrm{p}=$ pressure, $\mathrm{W}=$ work done, $\Gamma=$ torque, $\in=$ permittivity, $\mathrm{E}=$ electric field, $\mathrm{J}=$ current density, $\mathrm{L}=$ length.$\mathrm{v}=\frac{\pi \mathrm{pa}^{4}}{8 \eta \mathrm{L}}$$\mathrm...
Read More →Due to cold weather a 1m water pipe of cross-sectional area
Question: Due to cold weather a $1 \mathrm{~m}$ water pipe of cross-sectional area $1 \mathrm{~cm}^{2}$ is filled with ice at $-10^{\circ} \mathrm{C}$. Resistive heating is used to melt the ice. Current of $0.5 \mathrm{~A}$ is passed through $4 \mathrm{k} \Omega$ resistance. Assuming that all the heat produced is used for melting, what is the minimum time required? (Given latent heat of fusion for water/ice $=3.33 \times 10^{5} \mathrm{~J} \mathrm{~kg}^{-1}$, specific heat of ice $=2 \times 10^{...
Read More →Solve this following
Question: A circular coil of radius $8.0 \mathrm{~cm}$ and 20 turns is rotated about its vertical diameter with an angular speed of $50 \mathrm{rad} \mathrm{s}^{-1}$ in a uniform horizontal magnetic field of $3.0 \times 10^{-2}$ T. The maximum emf induced the coil will be $\ldots \ldots \ldots \times 10^{-2}$ volt (rounded off to the nearest integer) Solution: Maximum $\operatorname{emf} \varepsilon=\mathrm{N} \omega \mathrm{AB}$ $\mathrm{N}=20, \omega=50, \mathrm{~B}=3 \times 10^{-2} \mathrm{~T...
Read More →For an ideal gas the instantaneous change in pressure
Question: For an ideal gas the instantaneous change in pressure ' $p$ ' with volume ' $v$ ' is given by the equation $\frac{\mathrm{dp}}{\mathrm{dv}}=-\mathrm{ap}$. If $\mathrm{p}=\mathrm{p}_{0}$ at $\mathrm{v}=0$ is the given boundary condition, then the maximum temperature one mole of gas can attain is : (Here $R$ is the gas constant)$\frac{\mathrm{p}_{0}}{\mathrm{aeR}}$$\frac{\mathrm{ap}_{0}}{\mathrm{eR}}$infinity$0^{\circ} \mathrm{C}$Correct Option: 1 Solution: $\int_{p_{0}}^{p} \frac{d p}{p...
Read More →The acceleration due to gravity is found upto an accuracy of
Question: The acceleration due to gravity is found upto an accuracy of $4 \%$ on a planet. The energy supplied to a simple pendulum to known mass ' $m$ ' to undertake oscillations of time period $\mathrm{T}$ is being estimated. If time period is measured to an accuracy of $3 \%$, the accuracy to which $\mathrm{E}$ is known as .........\% Solution: $\mathrm{T}=2 \pi \sqrt{\frac{\ell}{\mathrm{g}}} \Rightarrow \ell=\frac{\mathrm{T}^{2} \mathrm{~g}}{4 \pi^{2}}$ $\mathrm{E}=\mathrm{mg} \ell \frac{\th...
Read More →A block of mass m slides on the wooden wedge, which in turn slides backward on the horizontal surface.
Question: A block of mass $m$ slides on the wooden wedge, which in turn slides backward on the horizontal surface. The acceleration of the block with respect to the wedge is: Given $\mathrm{m}=8 \mathrm{~kg}, \mathrm{M}=16 \mathrm{~kg}$ Assume all the surfaces shown in the figure to be frictionless. $\frac{4}{3} \mathrm{~g}$$\frac{6}{5} g$$\frac{3}{5} g$$\frac{2}{3} g$Correct Option: , 4 Solution: Let acceleration of wedge is $\mathrm{a}_{1}$ and acceleration of block w.r.t. wedge is $\mathrm{a}...
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