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The ratio of accelerations due to gravity \(\mathrm{g}_{1}: \mathrm{g}_{2}\) on the surfaces of two planets is \(5: 2\) and the ratio of their respective average densities \(\rho_{1}: \rho_{2}\) is \(2: 1\). What is the ratio of respective escape velocities \(v_{1}: v_{2}\) from the surface of the planets?

asked Dec 12, 2021 in Kinematics by kritika (90.1k points)

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The velocity \((v)\) of a particle \((\) under a force \(F)\) depends on its distance \((x)\) from the origin \((\) with \(x>0) v \propto \frac{1}{\sqrt{x}} .\) Find how the magnitude of the force \((F)\) on the particle depends on \(x\)

asked Dec 12, 2021 in Kinematics by kritika (90.1k points)

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In a triangle \(A B C\), the sides \(A B\) and \(A C\) are represented by the vectors \(3 \hat{i}+\hat{j}+\hat{k}\) and \(\hat{i}+2 \hat{j}+\hat{k}\) respectively. Calculate the angle \(\angle A B C\)

asked Dec 12, 2021 in Kinematics by kritika (90.1k points)

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A block of mass \(m_{2}\) is placed on a horizontal table and another block of mass \(m_{1}\) is placed on top of it. An increasing horizontal force \(F=\alpha t\) is exerted on the upper block but the lower block never moves as a result. If the co-efficient of friction between the blocks is \(\mu_{1}\) and that between the lower block and the table is \(\mu_{2}\), then what is the maximum possible value of \(\mu_{1} / \mu_{2}\) ?

asked Dec 12, 2021 in Kinematics by kritika (90.1k points)

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In case of a simple harmonic motion, if the velocity is plotted along the X-axis and the displacement (from the equilibrium position) is plotted along the Y-axis, the resultant curve happens to be an ellipse with the ratio: \(\frac{\text { major axis (along X) }}{\text { min or axis (along Y) }}=20 \pi\) What is the frequency of the simple harmonic motion ?

asked Dec 12, 2021 in Kinematics by kritika (90.1k points)

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An electron accelerated through a potential of \(10,000 \mathrm{~V}\) from rest has a de-Broglie wave length ' \(\lambda\) '. What should be the accelerating potential so that the wave length is doubled?

asked Dec 12, 2021 in Kinematics by kritika (90.1k points)

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If the half life of a radioactive nucleus is 3 days, nearly what fraction of the initial number of nuclei will decay on the \(3^{\text {rd }}\) day? (Given that \(\sqrt[3]{0.25} \approx 0.63\) )

asked Dec 12, 2021 in Kinematics by kritika (90.1k points)

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How the linear velocity 'v' of an electron in the Bohr orbit is related to its quantum number ' \(n\) ' ?

asked Dec 12, 2021 in Kinematics by kritika (90.1k points)

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If Young's double slit experiment is done with white light, which of the following statements will be true?

asked Dec 12, 2021 in Kinematics by kritika (90.1k points)

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There is a small air bubble at the centre of a solid glass sphere of radius ' \(r\) ' and refractive index ' \(\mu\) '. What will be the apparent distance of the bubble from the centre of the sphere, when viewed from outside ?

asked Dec 12, 2021 in Kinematics by kritika (90.1k points)

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A point source is placed at co-ordinates \((0,1)\) in \(X-Y\) plane. A ray of light from the source is reflected on a plane mirror placed along the X-axis and perpendicular to the X-Y plane. The reflected ray passes through the point \((3,3)\). What is the path length of the ray from \((0,1)\) to \((3,3)\) ?

asked Dec 12, 2021 in Kinematics by kritika (90.1k points)

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Four resistors \(100 \Omega, 200 \Omega, 300 \Omega\) and \(400 \Omega\) are connected to form four sides of a square. The resistors can be connected in any order. What is the maximum possible equivalent resistance across the diagonal of the square ?

asked Dec 12, 2021 in Kinematics by kritika (90.1k points)

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\(\mathrm{SiO}_{2}\) is attacked by which one / ones of the following?

asked Dec 11, 2021 in Some basic concepts in chemistry by kritika (90.1k points)

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Which of the following statement(s) is/are incorrect:

asked Dec 11, 2021 in Some basic concepts in chemistry by kritika (90.1k points)

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For spontaneous polymerization, which of the following is (are) correct?

asked Dec 11, 2021 in Some basic concepts in chemistry by kritika (90.1k points)

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\(\mathrm{CH}_{3}-\mathrm{O}-\mathrm{CH}_{2}-\mathrm{Cl} \stackrel{\mathrm{aq}^{-1-1 \mathrm{OH}}}{\rightarrow} \mathrm{CH}_{3}-\mathrm{O}-\mathrm{CH}_{2}-\mathrm{OH}\) Which information below regarding this reaction is applicable?

asked Dec 11, 2021 in Some basic concepts in chemistry by kritika (90.1k points)

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A homonuclear diatomic gas molecule shows 2-electron magnetic moment. The one-electron and two-electron reduced species obtained from above gas molecule can act as both oxidizing and reducing agents. When the gas molecule is one-electron oxidized the bond length decreases compared to the neutral molecule. The gas molecule is

asked Dec 11, 2021 in Some basic concepts in chemistry by kritika (90.1k points)

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A solution is saturated with \(\mathrm{SrCO}_{3}\) and \(\mathrm{SrF}_{2} .\) The \(\left[\mathrm{CO}_{3}{ }^{2-}\right]\) is found to be \(1.2 \times 10^{-3} \mathrm{M}\). The concentration of \(\mathrm{F}\) - in the solution would be

asked Dec 11, 2021 in Some basic concepts in chemistry by kritika (90.1k points)

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For a reaction \(2 \mathrm{~A}+\mathrm{B} \rightarrow \mathrm{P}\), when concentration of \(\mathrm{B}\) alone is doubled, \(\frac{\mathrm{t}_{1}}{2}\) does not change and when concentrations of both \(A\) and \(B\) is doubled, rate increases by a factor of 4 . The unit of rate constant is,

asked Dec 11, 2021 in Some basic concepts in chemistry by kritika (90.1k points)

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The total number of alkyl bromides (including stereoismers) formed in the reaction \(\mathrm{Me}_{3} \mathrm{C}-\mathrm{CH}=\mathrm{CH}_{2}+\mathrm{HBr} \rightarrow\) will be

asked Dec 11, 2021 in Some basic concepts in chemistry by kritika (90.1k points)

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