Answer:
1.33 rev/s
Explanation:
I(arms and leg in) = I₁ = 0.9kgm²
I(arms out and one leg extended) = I₂ = 2.9kgm²
W₁ = 4.3 rev/s
W₂ = ?
Neglecting any external force acting on the skater (air resistance and friction), external torque isn't acting on the system and the angular momentum remains constant.
L(in) = L(out)
L₁ = L₂
L = angular momentum
L = Iw
I₁ w₁ = I₂ w₂
w₂ = (I₁ * w₁) / I₂
w₂ = (0.9 * 4.3) / 2.9
w₂ = 1.33 rev/s
Answer:
B) 1.5 m/s
Explanation:
The apparent frequency will be enhanced due to Doppler effect
If f be the apparent frequency , F be the real frequency , V be the velocity of sound and v be the velocity of approaching submarine then f is given by
f = F \frac{V+v}{V-v}\\
\frac{f}{F} =\frac{V+v}{V-v}\\
\frac{f}{F}-1 =\frac{V+v}{V-v}-1\\
\Delta f = \frac{2vf}{V-v}\\
200=\frac{2\times v\times 100\times 1000}{1482-v}\\
v=1.48 m/s
Answer:
2.43 m
Explanation:
From the question given above, the following data were obtained:
Number of wave crest = 7
Time = 10 s
Distance between each crest = 2.43 m
Wavelength =?
The wavelength of a wave is simply defined as the distance between two crest or trough of a wave. This simply means that we can obtain the wavelength of a wave by calculating the distance between two crest i.e
Wavelength = distance between each crest.
From the question given above, we were told that the distance between each crest is 2.43 m.
Therefore, the wavelength of the wave is 2.43 m
Answer:
r = 4.44 m
Explanation:
For this exercise we use the Archimedes principle, which states that the buoyant force is equal to the weight of the dislodged fluid
B = ρ g V
Now let's use Newton's equilibrium relationship
B - W = 0
B = W
The weight of the system is the weight of the man and his accessories (W₁) plus the material weight of the ball (W)
σ = W / A
W = σ A
The area of a sphere is
A = 4π r²
W = W₁ + σ 4π r²
The volume of a sphere is
V = 4/3 π r³
Let's replace
ρ g 4/3 π r³ = W₁ + σ 4π r²
If we use the ideal gas equation
P V = n RT
P = ρ RT
ρ = P / RT
P / RT g 4/3 π r³ - σ 4 π r² = W₁
r² 4π (P/3RT r - σ) = W₁
Let's replace the values
r² 4π (1.01 10⁵ / (3 8.314 (70 + 273)) r - 0.060) = 13000
r² (11.81 r -0.060) = 13000 / 4pi
r² (11.81 r - 0.060) = 1034.51
As the independent term is very small we can despise it, to find the solution
r = 4.44 m