Answer:
D. N= 11. 22 rad/s (CW)
Explanation:
Given that
Form factor R = 8
Speed of sun gear = 5 rad/s (CW)
Speed of ring gear = 12 rad/s (CW)
Lets take speed of carrier gear is N
From Algebraic method ,the relationship between speed and form factor given as follows

here negative sign means that ring and sun gear rotates in opposite direction
Lets take CW as positive and ACW as negative.
Now by putting the values


N= 11. 22 rad/s (CW)
So the speed of carrier gear is 11.22 rad/s clockwise.
Answer:
a. Composition of Vector.
Explanation:
When a bird flies in the air, it stretches its wings into air and this movement helps it move in a certain direction. This is an example of composition of vector. Air strikes the wings in opposite direction and bird wing movement helps it move against the wind.
I believe it’s A bit I. could be wrong
Answer: a 8143.71 kJ/kg
b 393.15 K
Explanation:
This system is an isobaric process in which there is no change in pressure a quasistatic process where a pressure distribution exists
a since no change in pressure =0 the system does work thus
FOR HELIUM properties in standard thermodynamic chart
cv = 3.1 kJ/kgK
M = Molar mass = 4 kg/kmol
R = Universal gas constant = 8.314 kJ/kg K
cp ≈ cv +R /M = 3.1 + 8.314 /4 = 5.1785 kJ/kgK
Cp = cp * M = 5.1785 kJ/kgK * 4 kg/kmol = 20.714 kJ/kgkmol
T = 120 °C to Kelvin = 120 + 273.15k = 393.15 K
W =n Cp ΔT = 1 kmol * 20.714 kJ/kg kmol* 393.15 K = 8143.71 kJ/kg
b convert T °C = T K thus 120 + 273.15 K = 393.15 K
P₁/T₁ = P₂/T₂
200 kPa/ 393.15 K = 200 kPa/T₂
T₂ = 200 kPa * 393.15 K/ 200 kPa = 393.15 K or 120 k
Answer:
Proof is as follows
Proof:
Given that , 
<u>for any function f with period T, RMS is given by</u>
<u />
<u />
In our case, function is 
![RMS = \sqrt{\frac{1}{T}\int\limits^T_0 {[V_{ac} + V_{dc}]^{2} } \, dt }](https://tex.z-dn.net/?f=RMS%20%3D%20%5Csqrt%7B%5Cfrac%7B1%7D%7BT%7D%5Cint%5Climits%5ET_0%20%7B%5BV_%7Bac%7D%20%2B%20V_%7Bdc%7D%5D%5E%7B2%7D%20%7D%20%5C%2C%20dt%20%20%7D)
Now open the square term as follows
![RMS = \sqrt{\frac{1}{T}\int\limits^T_0 {[V_{ac}^{2} + V_{dc}^{2} + 2V_{dc}V_{ac}] } \, dt }](https://tex.z-dn.net/?f=RMS%20%3D%20%5Csqrt%7B%5Cfrac%7B1%7D%7BT%7D%5Cint%5Climits%5ET_0%20%7B%5BV_%7Bac%7D%5E%7B2%7D%20%2B%20V_%7Bdc%7D%5E%7B2%7D%20%2B%202V_%7Bdc%7DV_%7Bac%7D%5D%20%7D%20%5C%2C%20dt%20%20%7D)
Rearranging terms

You can see that
- second term is square of RMS value of Vac
- Third terms is average of VdcVac and given is that average of

so
![RMS = \sqrt{\frac{1}{T}TV_{dc}^{2} + [RMS~~ of~~ V_{ac}]^2 }](https://tex.z-dn.net/?f=RMS%20%3D%20%5Csqrt%7B%5Cfrac%7B1%7D%7BT%7DTV_%7Bdc%7D%5E%7B2%7D%20%20%20%2B%20%5BRMS~~%20of~~%20V_%7Bac%7D%5D%5E2%20%7D)
![RMS = \sqrt{V_{dc}^{2} + [RMS~~ of~~ V_{ac}]^2 }](https://tex.z-dn.net/?f=RMS%20%3D%20%5Csqrt%7BV_%7Bdc%7D%5E%7B2%7D%20%20%20%2B%20%5BRMS~~%20of~~%20V_%7Bac%7D%5D%5E2%20%7D)
So it has been proved that given expression for root mean square (RMS) is valid