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Let \(v_{n}\) and \(E_{n}\) be the respective speed and energy of an electron in the horbit of radius \(r_{n}\), in a hydrogen atom, as predicted by Bohr's model. Then
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Dec 14, 2021
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If \(\chi\) stands for the magnetic susceptibility of a substance,for its magnetic permeability and \(\mu_{0}\) for the permeability of free space, then
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Dec 14, 2021
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If the pressure, temperature and density of an ideal gas are denoted by \(\mathrm{P}, \mathrm{T}\) ancespectively, the velocity of sound in the gas is
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A bullet of mass \(4.2 \times 10^{2} \mathrm{~kg}\), moving at a speed of \(300 \mathrm{~ms}\), gets stuck into a block with a mass 9 times that of th bullet. If the block is free to move without any kind of friction, the heat generated in the process will be
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A block of mass \(1 \mathrm{~kg}\) starts from rest at \(\mathrm{x}=0\) and moves along the \(\mathrm{x}\)-axis under the action of a force \(\mathrm{F}=\mathrm{kt}\), where is time and \(k=1 \mathrm{Ns}^{-1}\). The distance the block will travel in 6 seconds is
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Three vectors \(\vec{A}=a \vec{i}+\vec{j}+k ; B=\vec{i}+b \vec{j}+k\) and \(\vec{C}=\vec{i}+j+c \vec{k}\) are mutually perpendicular \((\vec{i}, \vec{j}\) and \(\vec{k}\) are unit vectors along \(X, Y\) and \(Z\) axis respectively \() .\) The respective values of a, b and c are
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Dec 14, 2021
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Two particles \(A\) and \(B\) (both initially at rest) start moving towards each other under a mutual force of attraction. A the instant when the speed of \(A\) is \(v\) and the speed of \(B\) is \(2 v\), the speed of the centre of mass is
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Dec 14, 2021
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The dimension of the universal constant of gravitation \(G\) is
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When a semiconducting device is connected in series with a battery and a resistance, a current is found to flow in the circuit. If, however, the polarity of the battery is reversed, practically no current flows in the circuit. The device may be
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Radon-222 has a half-life of \(3.8\) days. If one starts with \(0.064 \mathrm{~kg}\) of Radon-222, the quantity of Radon-222 left aft er 19 days will be
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When light of frequency \(v_{1}\) is incident on a metal with work function \(W(w h e r e, h>W)\), the photocurrent falls to zerd at a stopping potential of \(\mathrm{V}_{1} .\) If the frequency of light is increased to \(\mathrm{v}_{2}\), the stopping potential changes to \(\mathrm{V}_{2}\). Therefore, the charge of an electron is given by
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The de Broglie wavelength of an electron is \(0.4 \times 10^{10} \mathrm{~m}\) when its kinetic energy is \(1.0 \mathrm{keV}\). Its wavelength will be \(1.0 \times 10^{-10} \mathrm{~m}\), when its kinetic energy is
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Two monochromatic coherent light beams \(A\) and \(B\) have intensities \(L\) and \(\frac{ L}{4}\)respectively. If these beams are super. posed, the maximum and minimum intensities will be
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Dec 14, 2021
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A proton is moving with a uniform velocity of \(\$ 0 \mathrm{~ns}^{-1}\) along the \(Y\)-axis, under the joint action of a magnetic field aloig \(Z\)-axis and an electric field of magnitude \(2 \times 10 \mathrm{Vm}^{-1}\) along the negativeX-axis. If the electric field is switched off, the proton starts moving in a circle. The radius of the circle is nearly \(\left(\right.\) given \(\frac{e}{m}\) ratio for proton \(\left.=10 \mathrm{Ckg}^{-1}\right)\)
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Dec 14, 2021
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The magnetic field due to a current in a straight wire segment of length \(\mathrm{L}\) at a point on its perpendicular bisector at a distance \(r(r>>L)\)
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A charge of \(0.8\) coulomb is divided into two charges \(Q_{1}\) and \(Q_{2}\). These are kept at a separation of \(30 \mathrm{~cm}\). The force on \(Q_{1}\) is maximum when
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Three capacitors of capacitance \(1.0,2.0\) and \(5.0 \mu \mathrm{F}\) are connected in series to a \(10 \mathrm{~V}\) source. The potential difference across the \(2.0 \mu \mathrm{F}\) capacitor is
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A positive charge \(Q\) is situated at the centre of a cube. The electric flux through any face of the cube is (in SI units)
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A solid rectangular sheet has two different coefficients of linear expansion \(\alpha_{1}\) and \(\alpha_{2}\) along its length and breadth respectively. The coefficient of surface expansion is (for \(\alpha_{1} t<<1, \alpha_{2} t<<1\) )
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Dec 14, 2021
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2 moles of an ideal monatomic gas is carried from a state \(\left(\mathrm{P}_{0}, \mathrm{~V}_{0}\right)\) to a state \(\left(2 \mathrm{P}_{0}, 2 \mathrm{~V}_{0}\right)\) along a straight line path in a \(P-V\) diagram. The amount of heat absorbed by the gas in the process is given by
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Dec 14, 2021
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