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New answer posted
5 months agoContributor-Level 10
T sin θ = (1/4πε? ) * q²/ (2lsinθ)²
T cos θ = mg
∴ tan θ = q² / (4πε? mg * 4l²sin²θ)
[tan θ ≈ θ, for small angle]
So, θ³ = q² / (16πε? mgl²)
θ = ( q² / (16πε? mgl²) )¹/³
Also separation = 2l sin θ ≈ 2lθ
= 2l ( q² / (16πε? mgl²) )¹/³
= ( 8q²l³ / (16πε? mgl²) )¹/³
= ( q²l / (2πε? mg) )¹/³
New answer posted
5 months agoContributor-Level 10
Each side of the square has a resistance of 16/4 = 4Ω.
The side AC has the 9V, 1Ω source.
The other three sides (AB, BD, DC) form a path with resistance 4+4+4 = 12Ω.
This is in parallel with the side AC (4Ω).
Total resistance of the loop part: (12*4)/ (12+4) = 48/16 = 3Ω.
Total resistance of the circuit: R_total = 3Ω + 1Ω (internal) = 4Ω.
Total current from source I = V/R_total = 9/4 A.
This current splits.
Current through path ABDC, I? = I * (R_AC / (R_ABDC + R_AC) = (9/4) * (4/16) = 9/16 A.
Potential at B: V_B = V_A - I? R_AB = 9 - (9/16)*4 = 9 - 9/4 = 27/4 V.
Potential at D: V_D = V_C + I? R_CD = 0 + (9/16)*4 = 9/4 V.
Potential drop a
New answer posted
5 months agoContributor-Level 10
τ = Iα
I = ½MR² = ½ (10) (0.2)² = 0.2 kgm²
α = (ωf - ωi)/Δt = (0 - 600*2π/60)/10 = -2π rad/s²
τ = |Iα| = 0.2 * 2π = 0.4π = 4π * 10? ¹ Nm
New answer posted
5 months agoContributor-Level 10
W = ∫Fxdy
W = ∫ (5y + 20)dy from 0 to 10
W = [5y²/2 + 20y] from 0 to 10
W = (5 (10)²/2 + 20 (10) - 0 = 250 + 200 = 450 J
New answer posted
5 months agoContributor-Level 10
Binding Energy = (Δm)c²
= [Zmp + (A-Z)mn - MAl]c²
= [ (13*1.00726 + 14*1.00866) - 27.18846] u
= [ (13.09438 + 14.12124) - 27.18846] u
= [27.21562 - 27.18846] u
= 0.02716 u
= 0.02716 x = 27.16x * 10? ³
New answer posted
5 months agoContributor-Level 9
C? = dQ/ndT = (dU + pdV)/ndT
= C? + (pdV/ndT)
C? - C? = pdV/ndT = R - For ideal Gas [Box: PV = nRT, pdV = nRdT]
C? - C? = 1.1R - For Non – Idea gas (for Real gas)
And Real gas behaves as ideal gas at high temperature & low pressure.
∴ T_B > T_A
New answer posted
5 months agoContributor-Level 10
v = ω√ (A² - x²)
K.E. = ½mv² = ½mω² (A² - x²)
Total Energy T.E = ½mω²A²
At x = A/2
K.E. = ½mω² (A² - (A/2)²) = ½mω²A² (3/4)
K.E./T.E. = (½mω²A² (3/4) / (½mω²A²) = 3/4
New answer posted
5 months agoContributor-Level 9
For adiabatic process
T? V? ¹ = T? V? ¹
⇒ T? (Al? )? ¹ = T? (Al? )? ¹
T? /T? = (l? /l? )? ¹ = (l? /l? )? /³? ¹ = (l? /l? )?
New answer posted
5 months ago
Contributor-Level 10
Applying nodal analysis at point X with potential xV:
(x-20)/5 + (x-0)/2 + (x-20)/5 = 0
2 (x-20) + 5x + 2 (x-20) = 0
9x - 80 = 0 => x = 80/9 V
Potential drop across 2Ω resistor = x = 80/9 V.
(Note: There seems to be a discrepancy in the provided solution and standard circuit analysis. The provided solution calculates the current junction, not a single point.)
The solution provided in the image calculates as:
(x-0)/5 + (x-20)/5 + (x-20)/2 = 0
2x + 2 (x-20) + 5 (x-20) = 0
9x - 140 = 0
=> x = 140/9 V
Potential drop across 2Ω = 20 - x = 20 - 140/9 = 40/9 V
New answer posted
5 months agoContributor-Level 10
By Einstein's equation of photoelectric effect,
hc/λ = hc/λ? + eVs
Now hc/λ = hc/λ? + e*4.8 . (i)
hc/ (2λ) = hc/λ? + e*1.6 . (ii)
Multiply (ii) by 2:
hc/λ = 2hc/λ? + e*3.2 . (iii)
Equating (i) and (iii):
hc/λ? + 4.8e = 2hc/λ? + 3.2e
1.6e = hc/λ?
Substitute this into (i)
hc/λ = 1.6e + 4.8e = 6.4e
Substitute this into (ii)
(6.4e)/2 = hc/λ? + 1.6e
3.2e = hc/λ? + 1.6e
1.6e = hc/λ?
From (i): hc/λ = hc/λ? + 3 (hc/λ? ) = 4hc/λ?
λ? = 4λ
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