Class 11th
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New answer posted
4 months agoContributor-Level 10
Bohr's model is too simple for atoms beyond hydrogen. In multi-electron atoms like helium, it fails because it ignores a couple of aspects. First is the electron-to-electron repulsion, and second is the shielding effect, where inner electrons reduce the nuclear pull on outer ones. Due to both, orbitals with the same principal quantum number don't have the same energy. Bohr's model of atom assumes that it should have the same energy.
New answer posted
4 months ago
Contributor-Level 10
We have to find the point where the gravitational field must be zero.
EG = 0
GM/x² = G (9M)/ (8R-x)²
1/x² = 9/ (8R-x)²
8R - x = 3x => x = 2R
Potential at A (surface of first planet), VA = -GM/R - G (9M)/7R = -16GM/7R
Potential at point x, Vx = -GM/x - G (9M)/ (8R-x) = -GM/2R - G (9M)/6R = -2GM/R
ΔV = Vx - VA = -2GM/R - (-16GM/7R) = (-14+16)GM/7R = 2GM/7R
Using conservation of mechanical energy
ΔKE = ΔU = mΔV
½mv² = m (2GM/7R)
v² = 4GM/7R
v = √ (4GM/7R) => a = 4
New answer posted
4 months agoContributor-Level 10
Loss in elastic potential energy = Gain in KE
½ (YA/L)x² = ½mv²
0.5 * (0.5*10? * 10? / 0.1) * (0.04)² = 20*10? ³ v²
0.5 * (5*10²) * 1.6*10? ³ = 20*10? ³ v²
0.4 = 20*10? ³ v²
v² = 20 => v = √20 ≈ 4.47 m/s
(Re-checking calculations)
0.5 * ( (0.5e9 * 1e-6) / 0.1) * (0.04)^2 = 0.5 * (5e2) * 1.6e-3 = 4.
0.5 * 20e-3 * v^2 = 10e-3 v^2
4 = 10e-3 v^2
v^2 = 400 => v = 20 m/s
New answer posted
4 months ago
Contributor-Level 9
Difference in Reading = Positive Zero Error - Negative Zero Error
= (+5) - [- (100-92)]
= 5 - [-8]
= 13
New answer posted
4 months agoContributor-Level 10
-dT/dt = K [T - Ts]
- (61-59)/4 = K [ (61+59)/2 - 30]
-0.5 = K [60 - 30] = 30K
So, K = -1/60 min? ¹
Again - (51-49)/t = K [ (51+49)/2 - 30]
-2/t = (-1/60) [50-30] = -20/60 = -1/3
t = 6 min
New answer posted
4 months agoContributor-Level 9
From conservation of momentum:
2*4 = 2v? + mv?
Given v? = 1 m/s (interpreted from intermediate steps)
8 = 2 (1) + mv?
mv? = 6 . (i)
From coefficient of restitution (e=1 for elastic collision):
e = (v? - v? )/ (u? - u? )
1 = (v? - v? )/ (4 - 0)
-1 = (v? - v? )/ (0 - 4) (as written in the image)
⇒ 4 = v? - 1
⇒ v? = 5 . (ii)
Put (2) in (1), m (5) = 6
m = 1.2kg
New answer posted
4 months agoContributor-Level 10
E = ½mω²a² . (i)
When KE = 3E/4, PE = E - KE = E/4
E/4 = ½mω²y² . (ii)
Divide eq? (i) by eq? (ii) we get
4 = a²/y² => y = a/2
New answer posted
4 months agoContributor-Level 10
h = u²/2g, u = √2gh
Now, S = h/3
S = ut + ½at²
h/3 = √2ght - ½gt²
t² - 2√ (2h/g)t + 2h/3g = 0
Using quadratic formula for t:
t = ( 2√ (2h/g) ± √ (8h/g) - 4 (2h/3g) / 2
t = √ (2h/g) ± √ (2h/g - 2h/3g) = √ (2h/g) ± √ (4h/3g)
t? /t? = (√ (2h/g) - √ (4h/3g) / (√ (2h/g) + √ (4h/3g)
t? /t? = (√2 - √ (4/3) / (√2 + √ (4/3) = (√6 - 2)/ (√6 + 2)
(Note: There is a calculation error in the provided solution. Re-evaluating the physics.)
h/3 = (√2gh)t - ½gt²
(g/2)t² - (√2gh)t + h/3 = 0
t = (√2gh ± √ (2gh - 4 (g/2) (h/3)/g = (√2gh ± √ (4gh/3)/g
t? /t? = (√2gh - 2√gh/√3)/ (√2gh + 2√gh/√3)
New answer posted
4 months agoContributor-Level 9
(1/2)mu² = (1/2)mv² + mgl (1-cosθ)
⇒ v² = u² - 2gl (1-cosθ)
⇒ v² = 3² - 2*10*0.5* (1 - 1/2)
⇒ v² = 9 - 5 = 4
v = 2m/s
New answer posted
4 months ago
Contributor-Level 9
ω = √k_eq/μ [μ = (m? )/ (m? +m? ) (Reduced mass)]
k_eq = (k * 4k)/ (k+4k) = 4k/5
ω = √ (4k/5) / (m? / (m? +m? )
= √ (4*20/5) / (0.2*0.8)/ (0.2+0.8)
= √ (16/0.16)
= 10 rad/s
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