Class 11th

The coordinates of centre of mass of a uniform flag shaped lamina (thin flat plate) of mass 4 $k g$ . (the coordinates of the same are shown in figure) are:

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Contributor-Level 9

$(0,3)$

$\begin{array}{r} {\overset{?}{r}}_{c m} = \frac{1 * (\frac{\hat{i}}{2} + \hat{j}) + 1 * (\hat{i} + \frac{5 \hat{j}}{2})}{2} \\ {\overset{?}{r}}_{c m} = \frac{3}{4} \hat{i} + \frac{7}{4} \hat{j} \end{array}$

$(0,0)$

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2 months ago

A box weighs $196 N$ on a spring balance at the north pole. Its weight recorded on the same balance if it is shifted to the equator is close to (Take $g = 10 {m s}^{- 2}$ at the north pole and the radius of the earth $= 6400 k m$ )

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Class 11th Physics Thermodynamics

Contributor-Level 10

$W_{equator} = W_{pole} - m ω^{2} R$

$\begin{array}{r} = 196 - 19.6 * {(\frac{2 π}{24 * 60 * 60})}^{2} * 6400 * 10^{3} \\ = 195.33 N \end{array}$

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2 months ago

Class 11th Chemistry

How does the Bohr model contradict the Heisenberg Uncertainty Principle?

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Syed Aquib Ur Rahman

Contributor-Level 10

Through Heisenberg's Uncertainty Principle, it's proven that you can't pin down where an electron is and how fast it's moving at the same time. The Bohr model did not look into this. The main reason for that thought was that it pictured electrons like little planets that would move in a loop around the nucleus. But that only works if you know both position and speed exactly. Nature doesn't let you do that. Add to it the fact that electrons also behave like waves, and the Bohr model just couldn't keep up. That's why scientists had to move on to the quantum model, which fits way better with how electrons actually act.

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2 months ago

Class 11th Chemistry

Why is it that you cannot observe the wave properties of everyday objects?

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Syed Aquib Ur Rahman

Contributor-Level 10

De Broglie had the idea that everything that moves has a bit of wave behaviour. Technically, that includes any person, a football, and even a bus. The catch is that for big things, the mass is so large that their wavelength is insanely tiny. It's so tiny it's impossible to notice. That's why you don't see a football spreading out like ripples when you kick it. Electrons though? They're super light, so their wavelengths are big enough for us to actually measure. And when scientists did experiments, such as electron diffraction, the electrons really did behave like waves. That was the proof De Broglie needed to show he was ri

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2 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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2 months ago

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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2 months ago

Class 11th 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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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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2 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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2 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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2 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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