Physics

A particle of mass $m$ is fixed to one end of a light spring having force constant $k$ and unstretched length $l$ . The other end is fixed. The system is given an angular speed $ω$ about the fixed end of the spring such that it rotates in a circle in gravity free space. Then the stretch in the spring is:

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Contributor-Level 9

$m ?^{2} (l + x) = k x$

$\begin{array}{r} (\frac{l}{x} + 1) = \frac{k}{m ?^{2}} \\ x = \frac{l m ?^{2}}{k - m ?^{2}} \end{array}$

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4 months ago

Physics Thermodynamics

Two ideal Carnot engines operate in cascade (all heat given up by one engine is used by the other engine to produce work) between temperatures, $T_{1}$ and $T_{2}$ . The temperature of the hot reservoir of the first engine is $T_{1}$ and the temperature of the cold reservoir of the second engine is $T_{2}$ . $T$ is temperature of the sink of first engine which is also the source for the second engine. How is $T$ related to $T_{1}$ and $T_{2}$ , if both the engines perform equal amount of work?

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Physics Electromagnetic Induction

Contributor-Level 10

$W = Q_{1} - Q_{2} = Q_{2} - Q_{3}$

$Q_{2} = \frac{Q_{1} + Q_{3}}{2}$

$2 = \frac{Q_{1}}{Q_{2}} + \frac{Q_{3}}{Q_{2}}$

$2 = \frac{T_{1}}{T} + \frac{T_{2}}{T}$

$T = \frac{T_{1} + T_{2}}{2}$

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4 months ago

A planar loop of wire rotates in a uniform magnetic field. Initially, at $t = 0$ , the plane of the loop is perpendicular to the magnetic field. If it rotates with a period of $10 s$ about an axis in its plane then the magnitude of induced emf will be maximum and minimum, respectively at:

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Contributor-Level 10

At any time $t$

$? = B A c o s ? \frac{π t}{5} (? ω = \frac{2 π}{T} = \frac{2 π}{10} = \frac{π}{5})$

$\frac{d ?}{d t} = - \frac{π}{5} B A s i n ? (\frac{π t}{5})$

$e = \frac{π}{5} B A s i n ? (\frac{π t}{5})$

e will be maximum when $\frac{π t}{5}$ is $\frac{π}{2}$

$t = 2.5 s e c$

e will be minimum when $\frac{π t}{5}$ is $π, 0$

$t = 0,5 s e c$

So, answer will be (1).

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4 months ago

A thermodynamic cycle $x y z x$ is shown on a $V - T$ diagram. The P-V diagram that best describes this cycle is: (diagrams are schematic and not to scale)

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Contributor-Level 9

Kindly consider the following Image

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4 months ago

Mass per unit are of a circular disc of radius a depends on the distance $r$ from its centre as $σ (r) = A + B r$ . The moment of inertia of the disc about the axis, perpendicular to the plane and passing through its centre is:

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Contributor-Level 10

Moment of inertia of ring

$d l = {d m r}^{2}$

$I = \int_{0}^{a} ? (A + B r) 2 π r d r π r^{2}$

$= 2 π A \int_{0}^{a} ? r^{3} d r + 2 π B \int_{0}^{a} ? r^{4} d r$

$= 2 π [A \frac{a^{4}}{4} + B \frac{a^{5}}{5}]$

= 2 π a^{4} [\frac{A}{4} + \frac{B a}{5}]

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4 months ago

A stationary observer receives sound from two identical tuning forks, one of which approaches and the other one recedes with the same speed (much les than the speed of sound). The observers hears 2 beats/sec. The oscillation frequency of each tuning fork is $v_{0} = 1400 H z$ and the velocity of sound in air is $350 m / s$ . The speed of each tuning fork is close to:

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Physics Physics Ray Optics and Optical Instruments

Contributor-Level 10

$f_{1} = f_{o} (\frac{v}{v - v_{s}}) f_{1} - f_{2} = 2$

$f_{2} = f_{o} (\frac{v}{v + v_{s}}) f_{0} v [\frac{v + v_{s} - (v - v_{s})}{v^{2} - v_{s}^{2}}] = 2; \frac{2 f_{0} v v_{s}}{v^{2} - v_{s}^{2}} = 2$

$? v_{s} ? v ∴ v_{s} = \frac{1}{4} m / s$

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4 months ago

A thin lens made of glass (refractive index $= 1.5$ ) of focal length $f = 16 c m$ is immersed in a liquid of refractive index 1.42. If its focal length in liquid is $f_{l}$ , then the ratio $f_{l}$ /f is closest to the integer:

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Contributor-Level 10

$\frac{1}{f} = (μ_{g} - 1) (\frac{1}{R_{1}} - \frac{1}{R_{2}})$

$\frac{1}{f_{l}} = (\frac{μ_{g}}{μ_{l}} - 1) (\frac{1}{R_{1}} - \frac{1}{R_{2}})$

(i) $\frac{f_{l}}{f} = \frac{μ_{g} - 1}{\frac{μ_{g}}{μ_{l}} - 1} = \frac{1.5 - 1}{\frac{1.5}{1.41} - 1} = 8.875 \approx 9$ .

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4 months ago

Physics Class 12th

Boolean relation at the output state-Y for the following circuits is:

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Contributor-Level 9

First part of figure shown is or GATE and Second part of figure shown is NOT GATE So, $Y_{P} = O R + N O T =$ NOR GATE $Y = \overset{?}{A + B} = \overline{A} \cdot \overline{B}$

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4 months ago

Physics Nuclei

An electron (of mass $m$ ) and a photon have the same energy $E$ in the range of a few eV. The ratio of the de-Broglie wavelength associated with the electron and the wavelength of the photon is ( $c =$ speed of light in vacuum)

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Physics Physics Ray Optics and Optical Instruments

Contributor-Level 10

$λ_{electron} = \frac{h}{\sqrt[]{2 m E}} \frac{λ_{electron}}{λ_{photon}} = \frac{1}{c} \sqrt[]{\frac{E}{2 m}}$

$λ_{photon} = \frac{h c}{E}$

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4 months ago

The critical angle of a medium for a specific wavelength, if the medium has relative permittivity 3 and relative permeability $\frac{4}{3}$ $\frac{}{}$ for this wavelength, will be

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