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11 months ago

Physics Communication Systems

Only 2% of the optical source frequency is the available channel bandwidth for an optical communicating system operating at 1000 nm. If an signal requires a bandwith of 8 kHz, how many channels can be accommodated for transmission:

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alok kumar singh

Contributor-Level 10

$v = f λ$

$f = \frac{v}{λ} = \frac{3 * 1 0^{8}}{1 0^{3} * 1 0^{- 9}} = 3 * 1 0^{14} H_{z}$

Channels = $\frac{2 % o f 3 * 1 0^{14} H_{z}}{8 * 1 0^{3}}$

$\frac{2 % o f 3 * 1 0^{14} H_{z}}{8 * 1 0^{3}}$

$\frac{= \frac{2 x}{100} 3 * 1 0^{14}}{8 * 1 0^{3}} = 75 * 1 0^{7}$

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11 months ago

Physics Physics Wave Optics

Using Young's double slit experiment, a monochromatic light of wavelength 5000 $\overset{o}{A}$ produces fringes of fringe width 0.5mm. If another monochromatic light of wavelength 6000 $\overset{o}{A}$ is used and the separation between the slits is doubled, then the new fringe width will be:

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alok kumar singh

Contributor-Level 10

$β_{1} = \frac{λ_{1} D_{1}}{d_{1}}$

$β_{2} = \frac{λ_{2} D_{2}}{d_{2}}$

$\frac{β_{1}}{β_{2}} = \frac{λ_{1}}{d_{1}} * \frac{d_{2}}{λ_{2}}$

$\frac{0.5}{β_{2}} = \frac{5000 * d_{1}}{d_{1} * 600}$

$β_{2} = \frac{0.5 * 6}{10}$

2 = 0.3mm

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11 months ago

Physics Physics Electrostatic Potential and Capacitance

A positive charge particle of 100mg is thrown in opposite direction to a uniform electric field of strength 1 * 10⁵ NC^-1, If the charge on the particle is $40 μ C$ and the initially velocity is 200 ms^-1, how much distance it will travel before coming to the rest momentarily:

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alok kumar singh

Contributor-Level 10

a = $\frac{q E}{m} = \frac{40 * 1 0^{? 6} * 1 0^{5}}{100 * 1 0^{? 3} * 1 0^{? 3}}$

= 40 * 10³ m/sec²

v² = u² + 2a s

$? 0 = {(200)}^{2} ? 2 * 40 * 1 0^{3} s$

$s = \frac{200 * 200}{2 * 40 * 1 0^{3}} = 0.5 m$

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Physics Physics Electrostatic Potential and Capacitance

A parallel plate capacitor filled with a medium of dielectric constant 10, is connected across a battery and is charged. The dielectric slab is replaced by another slab of dielectric constant 15. Then the energy of capacitor will:

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alok kumar singh

Contributor-Level 10

UI= $\frac{1}{2} c v^{2}$

$U_{i} = \frac{1}{2} \frac{\in_{0} A}{d} * k v^{2}$

$U_{i} = \frac{1}{2} \frac{\in_{0} A}{d} * 10 v^{2}$

$U_{f} = \frac{1}{2} \frac{\in_{0} A}{d} * 15 v^{2}$

$\frac{U_{f}}{U_{i}} = \frac{3}{2}$

$\frac{U_{f} - U_{i}}{U_{i}} * 100 = (\frac{3}{4} - 1) * 100$

$\frac{1}{2} * 100$

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11 months ago

Physics Waves

A longitudinal wave is represented by x = 10 sin 2p $(n t - \frac{x}{λ}) c m .$ The maximum particle velocity will be four times the wave velocity if the determined value of wavelength is equal to:

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alok kumar singh

Contributor-Level 10

x = 10 $2 ? (n t ? \frac{x}{?}) c m$

V (wave velocity) = $\frac{? ?}{2 ?}$

v_max = 10 * 2p n

10 * 2pn = 4 * $\frac{? ?}{2 ?}$

10 * 2pn = $4 \frac{2 ? ? n ?}{2 ?}$

x = 5?

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11 months ago

Physics Magnetism and Matter

At a certain place the angle of dip is 30° and the horizontal component of earth's magnetic field is 0.5 G. The earth's total magnetic field (in G), at the certain place, is:

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alok kumar singh

Contributor-Level 10

$B c o s δ = B_{H}$

B cos 30° = 0.5

$B = \frac{0 . * 2}{\sqrt[]{3}} = \frac{1}{\sqrt[]{3}}$

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11 months ago

Physics Gravitation

The escape velocity of a body on a planet 'A' is 12 kms^-1. The escape velocity of the body on another planet 'B', whose density is four times and radius is half of the planet 'A', is:

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alok kumar singh

Contributor-Level 10

$M_{A} = ρ_{A} * \frac{4}{3} π R_{A}^{3}$ $ρ_{B} = 4 ρ_{A}$

$M_{B} = ρ_{B} * \frac{4}{3} π R_{B}^{3}$ $R_{B} = \frac{R_{A}}{2}$

$\frac{M_{A}}{M_{B}} = 2, \frac{R_{A}}{R_{B}} = 2$ $\frac{V_{E A}}{V_{E B}} = \sqrt[]{\frac{2 G_{1} M_{A}}{R_{A}} * \frac{R_{B}}{2 G_{1} M_{B}}}$

$v_{E A} = v_{E B} = 12 k m s e c^{- 1}$

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11 months ago

Physics Motion in a Plane

Two vectors $\vec{A} a n d \vec{B}$ have equal magnitudes. If magnitude of $\vec{A} + \vec{B}$ is equal to two times the magnitude of $\vec{A} - \vec{B},$ then the angle between $\vec{A} a n d \vec{B}$ will be:

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alok kumar singh

Contributor-Level 10

$| \vec{A} + \vec{B} | = 2 | \vec{A} - \vec{B} |$

Given A = B

Squaring equation (1) both side.

${| \vec{A} + \vec{B} |}^{2} = {(2 | \vec{A} - \vec{B} |)}^{2}$

$A^{2} + B^{2} + 2 \vec{A} . \vec{B} = 4 (A^{2} + B^{2} - 2 \vec{A} . \vec{B})$

2A² + 2A² cosq = 4 (2A² – 2A² cosq)

2A² + 2A² cosq = 8A² – 8A² cosq

10A² cosq = 6A²

cosq = $\frac{3}{5}$

q = cos^-1 (3/5)

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11 months ago

Physics Thermal Properties of Matter

In van dar Wall equation $[P + \frac{a}{V^{2}}] [V - b] = R T; P$ is pressure, V is volume, R is universal gas constant and T is temperature. The ratio of constants $\frac{a}{b}$ is dimensionally equal to:

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alok kumar singh

Contributor-Level 10

dimension of a Pv²

$\frac{a}{b} = p v$ dimension of b = v

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11 months ago

Physics Laws of Motion

A block of metal weighing 2kg is resting on a frictionless plane (as shown in figure). It is struck by a jet relasing water at a rate of 1 kgs^-1 and at a speed of 10 ms^-1. Then, the initial acceleration of the block, in ms^-2, will be:

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alok kumar singh

Contributor-Level 10

$a = \frac{F}{m} = \frac{m v}{m} = \frac{1 * 10}{2} = 5 m / s e c^{2}$

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