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New answer posted
7 months agoContributor-Level 10
The force (F) exerted by radiation is the rate of change of momentum (p).
F = Δp/Δt
For photons, p = E/c. So, F = (1/c) * (ΔE/Δt).
Since Power (P) is ΔE/Δt, F = P/c.
Intensity (I) is Power per unit Area (P/A).
The formula provided in the document is F/A = (nE)/ (Δt c A) which leads to a final calculated value of 25 W/cm².
New answer posted
7 months agoContributor-Level 10
The formula for escape velocity (v_e) is v_e = √ (2GM/R).
According to the question, the new escape velocity (v_e') from a new radius R' is related to the original escape velocity by 10v_e' = v_e.
10 * √ (2GM/R') = √ (2GM/R)
Squaring both sides:
100 * (2GM/R') = (2GM/R)
100/R' = 1/R
R' = R/100
If R is the radius of Earth (6400 km), then:
R' = 6400 km / 100 = 64 km
New answer posted
7 months agoContributor-Level 10
The number of revolutions can be found using the rotational kinematic equation for angular displacement (θ):
θ = (ω_initial + ω_final)/2 * t
Number of revolutions = θ / 2π
Number of revolutions = [ (ω_final + ω_initial) * t] / (2 * 2π)
Based on the numerical values provided in the document, the calculation is:
Number of revolution = [ (2π * 3360/60 + 0) * t] / (2 * 2π) . with further calculation yielding the result:
Number of revolution = 728
New answer posted
7 months ago
Contributor-Level 10
The equations for an object rolling down an inclined plane without slipping are:
· Force equation: mg sinθ - f_s = ma
· Torque equation: f_s R = Iα
Since a = αR, we can write f_s = Iα/R = Ia/R².
Substituting this into the force equation:
mg sinθ - Ia/R² = ma
mg sinθ = a (m + I/R²)
a = (mg sinθ) / (m + I/R²)
The time taken to travel a distance S is given by S = ½ at², which means t ∝ 1/√a. Therefore, the object with the largest acceleration (a) will arrive first.
The problem is analyzed for different bodies:
· Ring: I =
New answer posted
7 months agoContributor-Level 10
Initial charge Q = CV = 14 * 10? ¹² * 12 = 168 * 10? ¹² C
Initial energy U_in = ½ CV² = ½ (14 * 10? ¹²) * 12² = 1008 pJ
When the battery is disconnected and a dielectric (k=7) is inserted, the new capacitance is C' = kC.
The charge Q remains constant.
Final energy U_f = Q²/2C' = Q²/ (2kC) = (CV)²/ (2kC) = CV²/ (2k)
U_f = (14 * 10? ¹² * 12²) / (2 * 7) = 144 pJ
Mechanical energy available for oscillation
New answer posted
7 months agoContributor-Level 10
R_eq = R? + R?
L_total / (K_eq * A) = L? / (K? A) + L? / (K? A)
Assuming L? = L? = l, L_total = 2l
2l / (K_eq * A) = l/ (K? A) + l/ (K? A)
2/K_eq = 1/K? + 1/K? = (K? + K? )/ (K? )
K_eq = 2K? K? / (K? + K? )
New answer posted
7 months agoContributor-Level 10
U = U? + U? = (n? /N_A) (F? R/2)T? + (n? /N_A) (F? R/2)T?
For the mixture: U = (n? +n? )/N_A * (FR/2)T
F = (n? F? + n? F? ) / (n? + n? )
Equating the expressions for U and solving for T gives:
T = (n? F? T? + n? F? T? ) / (n? F? + n? F? )
New answer posted
7 months agoContributor-Level 10
I = I? sin (ωt) + I? cos (ωt)
This can be written as I = I? sin (ωt + φ), where I? = √ (I? ² + I? ²)
A hot wire ammeter reads the rms value of the current.
I_rms = I? /√2 = √ (I? ² + I? ²)/√2
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