Physics

Contributor-Level 9

T = 2π√ (l/g) ⇒ g = 4π²l/T²
Percentage error: Δg/g = Δl/l + 2 (ΔT/T) = (0.1/10.0) + 2 (0.005/0.5) = 0.03
Percentage error = (Δg/g) * 100 = 3%
ω = 2πf = 100π rad/s
i_rms = i? /√2
While current changes from its maximum to its rms value, its phase changes by π/4 rad.
t = (π/4)/ω = π/ (4 * 100π) = 2.5 * 10? ³ s = 2.5ms.

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7 months ago

A boy of mass 4 kg is standing on a piece of wood having mass 5 kg. If the coefficient of friction between the wood and the floor is 0.5, the maximum force that boy can exert on the rope so that the piece of wood does not move from its place is _____ N. (Round off to the Nearest Integer) [Take g = 10 ms?²]

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Physics Units and Measurement

Contributor-Level 10

Assuming the rope in the boy's hand is vertical and using a Free Body Diagram (FBD):
f? = T
R + T = 90 ⇒ R = 90 - T
For the piece of wood not to move, f? ≤ µR:
T ≤ 0.5 (90 - T) ⇒ T ≤ 30N

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7 months ago

The time period of a simple pendulum is given by T = 2π√(l/g). The measured value of the length of pendulum is 10cm known to a 1 mm accuracy. The time for 200 oscillations of the pendulum is found to be 100 second using a clock of 1 s resolution. The percentage accuracy in the determination of 'g' using this pendulum is 'x'. The value of 'x' to the nearest integer is,

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Physics Physics Ray Optics and Optical Instruments

Contributor-Level 9

l = 10.0 ± 0.1cm.
T = (100 ± 1) / 200 = 0.5 ± 0.005

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7 months ago

The image of an object placed in air formed by a convex refracting surface is at a distance of 10 m behind the surface. The image is real and is at 2/3 of the distance of the object from the surface. The wavelength of light inside the surface is 2/3 times the wavelength in air. The radius of the curved surface is x/13 m. The value of 'x' is _____.

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Physics Physics Alternating Current

Contributor-Level 10

Given the refractive index μ = λ? / λ = 3/2 and v = 10m, the object distance is u = - (3/2)v = -15m.
Using the lens maker's formula:
μ/v - 1/u = (μ - 1)/R
(3/2)/10 - 1/ (-15) = (3/2 - 1)/R
This gives the radius of curvature R:
R = -30/13 m

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7 months ago

In a series LCR resonance circuit, if we change the resistance only, from a lower to higher value :

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Contributor-Level 9

Resonance frequency is independent of R.
Quality factor = ωL/R ⇒ Quality factor decreases with increase in R.
Bandwidth of resonance circuit = R/L ⇒ increases with increase in R.

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7 months ago

The disc of mass M with uniform surface mass density σ is shown in the figure. The centre of mass of the quarter disc (the shaded area) is at the position (xa/3π, xa/3π) where x is---------. (Round off to the Nearest integer) [a is an area as shown in the figure]

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Contributor-Level 10

The x and y coordinates of the center of mass are given by:
x? = y? = 4a / 3π

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7 months ago

A body of mass 1 kg rests on a horizontal floor with which it has a coefficient of static friction 1/√3. It is desired to make the body move by applying the minimum possible force F N. The value of F will be ______. (Round off to Nearest Integer) [Take g = 10 ms?²]

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Physics Physics Electrostatic Potential and Capacitance

Contributor-Level 10

The minimum force F? is calculated as:
F? = (μmg) / √* (1 + μ²)* = ( (1/√3) * 1 * 10 ) / √* (1 + (1/√3)²) = 5N

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7 months ago

A 2 µF capacitor C₁ is first charged to a potential difference of 10V using a battery. Then the battery is removed and the capacitor is connected to an uncharged capacitor C₂ of 8 µF. The charge in C₂ on equilibrium condition is --------- µC. (Round off to the Nearest integer)

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Physics Dual Nature of Radiation and Matter

Contributor-Level 10

Let the charge on C? be q µC. For the capacitor network:
q/C? = (C? * 10 - q) / C? ⇒ q/8 = (2 * 10 - q) / 2 ⇒ q = 16

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7 months ago

A particle is traveling 4 times as fast as an electron. Assuming the ratio of de- Broglie wavelength of a particle to that of electron is 2 : 1, the mass of the particle is :

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Contributor-Level 9

λ? /λ? = (m? v? ) / (m? v? ) ⇒ m? = m? (v? /v? ) (λ? /λ? ) = m? (1/4) (1/2) = (1/8)m?

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7 months ago

Two particles A and B of equal masses are suspended from two massless springs of spring constants K₁ and K₂ respectively. If the maximum velocities during oscillations are equal, the ratio of the amplitude of A and B is

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