Physics

Contributor-Level 10

F = Gm²/ (2R)² = mω²R Given m = 1kg
⇒ ω² = Gm/ (4R³)
⇒ ω = (1/2)√ (G/R³)

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10 months ago

The resistance of a conductor at 15°C is 16Ω and at 100°C is 20Ω. What will be the temperature coefficient of resistance of the conductor?

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Contributor-Level 10

R = R? [1 + α? T]
⇒ 16 = R? [1 + α (15 - T? )]
20 = R? [1 + α (100 - T? )]
Assuming T? = 0°C:
16 = R? (1 + 15α)
20 = R? (1 + 100α)
Dividing the equations:
16/20 = (1+15α)/ (1+100α)
16 + 1600α = 20 + 300α
1300α = 4
α = 4/1300 ≈ 0.003 °C? ¹

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10 months ago

Figure A and B show long straight wires of circular cross section (a and b with a < b), carrying current I which is uniformly distributed across the cross section. The magnitude of magnetic field B varies with radius r and can be represented as:

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Physics Mechanical Properties of Fluids

Contributor-Level 10

As b > a
The magnetic field inside the wire (rR) is B = µ? I/ (2πr).
For wire with radius a, B increases linearly to r=a, then decreases. For wire with radius b, B increases linearly to r=b, then decreases. Since a⇒ B? > B?
B? = µ? I / 2πa
B? = µ? I / 2πb
(Note: The question is likely asking for the graph representation, which is option A based on the formulas.)

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10 months ago

A raindrop with radius R = 0.2 mm falls from a cloud at a height h = 2000 m above the ground. Assume that the drop is spherical through its fall and the force of buoyance may be neglected, then the terminal speed attained by the raindrop is :
[Density of water ρw = 1000 kg m⁻³, and Density of air ρa = 1.2 kg m⁻³, g = 10 m/s², Coefficient of viscosity of air η = 1.8 * 10⁻⁵ Nsm⁻²]

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Contributor-Level 10

At terminal speed
Mg = Fv = 6πηRv
⇒ V = mg / 6πηR
V = (4/3)πR³ρg / 6πηR
⇒ V = (2/9) * (ρR²g/η)
= (2/9) * (1000 * (0.2 * 10? ³)² * 10) / (1.8 * 10? )
= 4.94 m/s

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10 months ago

Physics Class 11th

The planet Mars has two moons, if one of them has a period 7 hours, 30 minutes and an orbital radius of 9.0 * 10³ km. Find the mass of Mars.
{Given 4π²/G = 6 * 10¹¹ N⁻²kg²}

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Contributor-Level 10

T² = (4π²r³)/GM
⇒ M = (4π²r³)/ (G T²)
⇒ M = 6 * 10¹¹ * (9 * 10? )³ / (450 * 60)²
= 6.48 x 10²³ kg
(Note: There is a calculation error in the source image. Using the formula and given values: M = (6e11 * (9e6)^3) / (27000)^2 = 6e23 kg)

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10 months ago

The nuclear activity of a radioactive element becomes (1/8)ᵗʰ of its initial value in 30 years. The half –life of radioactive element is __________ years.

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Contributor-Level 10

A = A? (1/2)?
A/A? = 1/8 = (1/2)³ ⇒ n = 3
t = n T½
30 = 3 T½
T½ = 10 years

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10 months ago

In a semiconductor, the number density of intrinsic charge carriers at 27°C is 1.5 * 10¹? / m³. If the semiconductor is doped with impurity atom, the hole density increases to 4.5*10²² / m³. The electron density in the doped semiconductor is __________ x 10? / m³.

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Contributor-Level 10

ni² = ne * nh
(1.5*10¹? )² = ne * (4.5*10²²)
ne = (2.25 * 10³²)/ (4.5 * 10²²) = 0.5 * 10¹? = 5 * 10? / m³

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10 months ago

A system consists of two types of gas molecules A and B having same number density 2*10²⁵ / m³. The diameter of A and B are 10 Å and 5 Å respectively. They suffer collision at room temperature. The ratio of average distance covered by the molecule A to that of B between two successive collision is __________ x10⁻².

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Contributor-Level 10

Mean free path:
λ ∝ 1/ (nd²)
λA/λB = (d_B²/d_A²) = (5²/10²) = 25/100 = 25 * 10? ²

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10 months ago

A message single of frequency 20 kHz and peak voltage of 20 volt is used to modulate a carrier wave of frequency 1 MHz and peak voltage of 20 volt. The modulation index will be __________.

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Physics Dual Nature of Radiation and Matter

Contributor-Level 10

Modulation Index
μ = Am/Ac = 20/20 = 1

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10 months ago

A light beam of wavelength 500 nm is incident on a metal having work function of 1.25 eV, placed in a magnetic field of intensity B. The electrons emitted perpendicular to the magnetic field B, with maximum kinetic energy are bent into circular arc of radius 30cm. The value of B is __________ x x 10⁻⁷ T
Given hc = 20 * 10?²? J-m, mass of electron = 9 * 10⁻³¹ kg

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