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A Laser light of wavelength 660 nm is used to weld Retina detachment.  If a Laser pulse of width 60 ms and power 0.5 kW is used the approximate number of photons in the pulse are : [Take Planck’s constant h=6.62×10−34 Js] Option: 1  1020 Option: 2 1018 Option: 3 1022 Option: 4 1019

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A signal of frequency 20 kHz and peak voltage of 5 Volt is used to modulate a carrier wave of frequency 1.2 MHz and peak voltage 25 Volts.  Choose the correct statement. Option: 1  Modulation index=5, side frequency bands are at 1400 kHz and 1000 kHz Option: 2 Modulation index=5, side frequency bands are at 21.2 kHz and 18.8 kHz Option: 3 Modulation index=0.8, side frequency bands are at 1180 kHz and 1220 kHz Option: 4 Modulation index=0.2, side frequency bands are at 1220 kHz and 1180 kHz

$\\\text{ Modulate}\ Index: \frac{5}{25}=\frac{1}{5}=0.2\\ \text{Side frequency} (1200+20) H z=1220 k H z \ and \ 1200-20=1180 k H z$

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Two wires W1 and W2 have the same radius r and respective densities ρ1 and ρ2 such that ρ2=4ρ1.  They are joined together at the point O, as shown in the figure.  The combination is used as a sonometer wire and kept under tension T. The point O is midway between the two bridges.  When a stationary wave is set up in the composite wire, the joint is found to be a node.  The ratio of the number of antinodes formed in W1 to W2 is :   Option: 1  1 : 1 Option: 2  1 : 2 Option: 3  1 : 3 Option: 4 4 : 1

When the joint is found to be a node.

then the frequency is given as

$n=\frac{p}{2 l} \sqrt{\frac{T}{\pi r^{2} d}}$

Where p is also equal to the number of antinodes formed  in the wire

As

\begin{aligned} &n_{1}=n_{2}\\ &T \rightarrow \text { same }\\ &r \rightarrow \text { same }\\ &l \rightarrow \text { same } \end{aligned}

So

\begin{aligned} &\frac{p_{1}}{\sqrt{d_{1}}}=\frac{p_{2}}{\sqrt{d_{2}}}\\ &\frac{p_{1}}{p_{2}}=\frac{1}{2} \end{aligned}

A one metre long (both ends open) organ pipe is kept in a gas that has double the density of air at STP. Assuming the speed of sound in air at STP is , the frequency difference between the fundamental and second harmonic of this pipe is ________Hz.  Option: 1 106 Option: 2 600 Option: 3 310 Option: 4 210

So the answer will be 106

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If the magnetic field in a plane electromagnetic wave is given by $\vec B=3\times10^{-8} sin (1.6\times10^3x + 48\times10^{10}t)\ \vec{j} \ T$; then what will be the expression for the electric field? Option: 1   Option: 2  Option: 3    Option: 4

Nature of Electromagnetic Waves -

It is also seen from Maxwell’s equations that the magnitude of the electric and the magnetic fields in an electromagnetic wave are related as - $B_{0}= \frac{E_o}{c}$

given, $\vec B=3\times10^{-8} sin (1.6\times10^3x + 48\times10^{10}t)T$

\begin{aligned} \\ \left | \vec E \right |=BC=3\times10^{-8} sin (1.6\times10^3x + 48\times10^{10}t)\times (3\times10^8)\\ =9 sin (1.6\times10^3x + 48\times10^{10}t)T \end{aligned}

wave is propagating in -x direction, i.e., in - i direction.

the direction of the EMW wave is in the direction of $\vec E\times \vec B$.

Since B is in j direction and EMW is in -i direction. Therefore E is in (k) direction.

So Option (1) is correct.

A plane electromagnetic wave is propagating along the direction $\frac{\hat{i}+\hat{j}}{\sqrt{2}},$ with its polarization along the direction $\hat{k}.$ The correct form the magnetic field of the wave would be (here $B_{0}$ is an appropriate constant ) : Option: 1       Option: 2   Option: 3         Option: 4

EM wave is in direction - $\frac{\hat{i}+\hat{j}}{\sqrt{2}}$

As we know that the axis of polarisation of the Em wave is same as Electric field direction that is -  $\hat{k}$

$\vec{E}\times \vec{B}$ direction of propagation of EM wave = $\frac{\hat{i}+\hat{j}}{\sqrt{2}}$

$\Rightarrow \vec{k}\times \vec{B}=\frac{\hat{i}+\hat{j}}{\sqrt{2}}$

So  B is along                 $\frac{\hat{i}-\hat{j}}{\sqrt{2}}$

And the equation of the electromagnetic waves will be in terms of the  $\cos (\omega t-\vec{K}\cdot \vec{r})$

So by concluding the above result we can deduce that the option (1) is correct.

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A wire of length L and mass per unit length $6.0\times 10^{-3}kgm^{-1}$ is put under tension of 540 N. Two consecutive frequencies at which it resonates are : 420 Hz and 490 Hz . Then L in meters is : Option: 1 2.1 Option: 2 8.1 Option: 3 1.1 Option: 4 5.1

Fundamental frequency   = 490 – 420 = 70 Hz

$70=\frac{1}{2l}\sqrt{\frac{T}{\mu }}$

$\inline \Rightarrow 70=\frac{1}{2l}\sqrt{\frac{540}{6\times 10^{-3} }}$

$\inline \Rightarrow l=\frac{1}{2\times 70}\sqrt{90\times 10^{3}}=\frac{300}{140}$

$\inline \Rightarrow l\approx 2.14m$

Hence the correct option is (1).

Three harmonic waves having equal frequency v and same intensity I0, have phase angles 0, $\frac{\pi}{4}$ and $-\frac{\pi}{4}$ , respectively. When they are superimposed the intensity of the resultant wave is close to: Option: 1 0.2I0 Option: 2  I0 Option: 3 3I0 Option: 4 5.8I0

$A_{res} = A + \frac{A}{\sqrt2} + \frac{A}{\sqrt2} = A(1 + \sqrt2)$

$I = (1 + \sqrt2)^2I_0 = 5.8I_0$

Hence the correct option is (4).

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A transverse wave travels on a taut steel wire with a velocity of v when tension in it is 2.06 x 104 N . When the tension is changed to t, the velocity changed to v/2. The value of T (in N ) is close to : Option: 1 5.15 x 103  Option: 2 10.2 x 102  Option: 3 2.50 x 104  Option: 4 30.5 x 104

Velocity

$\\v\propto\sqrt{T}\\\\\frac{T_1}{T_2}=(\frac{v_1}{v_2})^2\\\\\frac{T_1}{T_2}=(\frac{v}{v/2})^2=4\\\\\Rightarrow T_2=\frac{T_1}{4}=0.515\times10^4\\T_2=5.15\times10^3 N$

Hence the correct option is (1)

A plane electromagnetic wave of frequency 25 GHz is propagating in vacuum along the z-direction. At a particular point in space and time, the magnetic field is given by $\overrightarrow{B} = 5 \times 10^{-8} \widehat{j} T$. The corresponding electric field $\overrightarrow{E}$ is (speed of light c = 3 x 108 ms-1) Option: 1 Option: 2  Option: 3  Option: 4

$\begin{array}{l}{\frac{E}{B}=c} \\ {E=B \times c} \\ {=15 \hat{i} \ \mathrm{V/m}}\end{array}$

Hence the correct option is (4).