Class 11th

Contributor-Level 9

In case of adiabatic process -

$W o r k d o n e, W = \frac{η R (T_{2} - T_{1})}{1 - Y}$

$A s, Δ Q = Δ U + W$

for adiabatic process :- $Δ Q = 0$

$\Rightarrow Δ U = - W$

So, when work is done by the gas, temperature decreases and when work is done on the gas, temperature rises.

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A water drop of diameter 2 cm is broken into 64 equal droplets. The surface tension of water is 0.075N/m. In this process the gain in surface energy will be:

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Contributor-Level 9

Gain in surface energy, $Δ U = T Δ A$

from volume centenary, $\frac{4}{3} π R^{3} = 64 * \frac{4}{3} π r^{3}$

$\Rightarrow r = \frac{R}{4}$

Initial surface area, Ai = 4pR²

final surface area, $A_{f} = 64 * 4 π r^{2}$

$∴ Δ U = 12 π R^{2} . T = 0.075 * 12 * 3.14 * 1 0^{- 4} = 2.8 * 1 0^{- 4} J$

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Two planets A and B of equal mass are having their period of revolutions T_A and T_B such that T_A = 2T_B. These planets are revolving in the circular orbits or radii r_A and r_B respectively. Which out of the following would be the correct relationship of their orbits?

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Contributor-Level 9

According to kepler's third law of time period –

${(\frac{T_{A}}{T_{B}})}^{2} = {(\frac{r_{A}}{r_{B}})}^{3} \Rightarrow \frac{r_{A}}{r_{B}} = 4^{1 / 3}$

$\Rightarrow r_{4}^{3} = 4 r_{B}^{3}$

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Match List – I with List – II

Choose the correct answer from the options given below:

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Class 11th Physics Motion in Plane

Contributor-Level 9

Use formula for M.I.

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Motion of a particle in x – y plane is described by a set of following equations x = 4sin $(\frac{π}{2} - ω t)$ m and y = 4sin $(ω t) m .$ The path of a particle will be:

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Class 11th Structure of Atom

Contributor-Level 9

$x = 4 s i n (\frac{π}{2} - ω t)$ - (i)

$y = 4 s i n (ω t)$ - (ii)

From (i) and (ii) cos^{2
$ω t + s i n^{2} ω t = {(\frac{x}{4})}^{2} + {(\frac{y}{4})}^{2} = 1$}

$\Rightarrow x^{2} + y^{2} = {(4)}^{2}$

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Which of the following is the correct plot for the probability density $ψ^{2} (r)$ as a function of distance 'r' of the electron from the nucleus for 2s orbital?

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Class 11th Work, Energy and Power

Contributor-Level 10

For 2S, number of radial moles = $n - l - 1 = 2 - 0 - 1 = 1$ and $Ψ^{2} (r)$ will always be positive

$∴ o p t i o n (B) i s c o r r e c t ?$ it has one radial node and it is positive.

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A particle of mass m is moving in a circular path of constant radius r such that its centripetal acceleration (a) is varying with time t as a = k² rt², where k is a constant. The power delivered to the particle by the force acting on it is given as

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Class 11th Chemistry Some Basic Concepts of Chemistry

Contributor-Level 9

a = k2rt2

$\Rightarrow \frac{v^{2}}{r} = k^{2} r t^{2}$

$\Rightarrow v = k r t$

$a_{t} = \frac{d v}{d t} = k r$

? tangential force, F_t = ma_t = mkr

$∴ P o w e r d e l i v e r e d, P = F_{t} v = (m k r) (k r t) = m k^{2} r^{2} t$

Note ® Power delivered by centripetal force will be zero.

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Using the rules for significant figures, the correct answer for the expression ^{$\frac{0.02858 * 0.112}{0.5702}$}will be

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Contributor-Level 10

Kindly go through the solution

$\frac{0.02858 * 0.112}{0.5702} = 0.0561$

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The momentum of inertia of a uniform thin rod about a perpendicular axis passing through on end is I₁. The same rod is into a ring and its moment of inertia about a diameter is I₂. If $\frac{I_{1}}{I_{2}} i s \frac{X π^{2}}{3},$ then the value of x will be__________.

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Class 11th Physics Oscillations

Contributor-Level 10

According to question, we can write

$l = 2 π r \Rightarrow r = \frac{l}{2 π}$

$I_{1} = \frac{m l^{2}}{3}, a n d I_{2} = \frac{m r^{2}}{2} = \frac{m l^{2}}{8 π^{2}}$

$\Rightarrow \frac{I_{1}}{I_{2}} = \frac{m l^{2}}{3} * \frac{8 π^{2}}{m l^{2}} = \frac{8 π^{2}}{3}$

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In an experiment to determine the velocity of sound in air at room temperature using a resonance tube, the first resonance is observed when the air column has a length of 20.0 cm for a tuning form of frequency 400 Hz is used. The velocity of the sound at room temperature is 336 ms^-¹. The third resonance is observed when the air column has a length of ____________cm.

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