Answer:
0.09 N
Explanation:
We are given that
Radius of disk,r=6 cm=![\frac{6}{100}=0.06 m](https://tex.z-dn.net/?f=%5Cfrac%7B6%7D%7B100%7D%3D0.06%20m)
1 m=100 cm
B=1 T
Current,I=3 A
We have to find the frictional force at the rim between the stationary electrical contact and the rotating rim.
![dF=IBdr](https://tex.z-dn.net/?f=dF%3DIBdr)
![dF=IBdr](https://tex.z-dn.net/?f=dF%3DIBdr)
![\tau=rdF=IBrdr](https://tex.z-dn.net/?f=%5Ctau%3DrdF%3DIBrdr)
![\tau=\int_{0}^{R}IBr dr](https://tex.z-dn.net/?f=%5Ctau%3D%5Cint_%7B0%7D%5E%7BR%7DIBr%20dr)
![\tau=IB(\frac{R^2}{2}](https://tex.z-dn.net/?f=%5Ctau%3DIB%28%5Cfrac%7BR%5E2%7D%7B2%7D)
Torque due to friction
![\tau=R\times F](https://tex.z-dn.net/?f=%5Ctau%3DR%5Ctimes%20F)
Where friction force=F
![R\times F=\frac{IBR^2}{2}](https://tex.z-dn.net/?f=R%5Ctimes%20F%3D%5Cfrac%7BIBR%5E2%7D%7B2%7D)
![F=\frac{IBR}{2}](https://tex.z-dn.net/?f=F%3D%5Cfrac%7BIBR%7D%7B2%7D)
Substitute the values
![F=\frac{3\times 1\times 0.06}{2}](https://tex.z-dn.net/?f=F%3D%5Cfrac%7B3%5Ctimes%201%5Ctimes%200.06%7D%7B2%7D)
![F=0.09 N](https://tex.z-dn.net/?f=F%3D0.09%20N)
Answer:A
Explanation:
Engines in car are 4 stroke engine . A 4-stroke engine is internal combustion engine which derives its power by four piston strokes . Internal combustion means combustion takes inside the engine i.e. is in cylinder.
There are process in 4 stroke engine
- Intake: Intake of air
- Compression:compression of intake air to a high pressure
- Combustion:Fuel is injected and burned to get power
- Exhaust:removal of exhaust gases after combustion
67.8 turns needed by the secondary coil to run the bulb.
<u>Explanation</u>:
We know that,
![\text { Electric power }(p)=\frac{V^{2}}{R}](https://tex.z-dn.net/?f=%5Ctext%20%7B%20Electric%20power%20%7D%28p%29%3D%5Cfrac%7BV%5E%7B2%7D%7D%7BR%7D)
![\text { Hence, } \frac{P_{1}}{P_{2}}=\frac{V_{1}^{2} / R}{V_{2}^{2} / R}](https://tex.z-dn.net/?f=%5Ctext%20%7B%20Hence%2C%20%7D%20%5Cfrac%7BP_%7B1%7D%7D%7BP_%7B2%7D%7D%3D%5Cfrac%7BV_%7B1%7D%5E%7B2%7D%20%2F%20R%7D%7BV_%7B2%7D%5E%7B2%7D%20%2F%20R%7D)
![\frac{P_{1}}{P_{2}}=\frac{V_{1}^{2}}{V_{2}^{2}}](https://tex.z-dn.net/?f=%5Cfrac%7BP_%7B1%7D%7D%7BP_%7B2%7D%7D%3D%5Cfrac%7BV_%7B1%7D%5E%7B2%7D%7D%7BV_%7B2%7D%5E%7B2%7D%7D)
For calculating number of turns
![\frac{N_{P}}{N_{S}}=\frac{V_{P}}{V_{S}}](https://tex.z-dn.net/?f=%5Cfrac%7BN_%7BP%7D%7D%7BN_%7BS%7D%7D%3D%5Cfrac%7BV_%7BP%7D%7D%7BV_%7BS%7D%7D)
Given that,
![80 \mathrm{W}\left(P_{1}\right) \text { bulb with voltage } 120 \mathrm{V}\left(V_{1}\right) \text { is connected to a transformer. }](https://tex.z-dn.net/?f=80%20%5Cmathrm%7BW%7D%5Cleft%28P_%7B1%7D%5Cright%29%20%5Ctext%20%7B%20bulb%20with%20voltage%20%7D%20120%20%5Cmathrm%7BV%7D%5Cleft%28V_%7B1%7D%5Cright%29%20%5Ctext%20%7B%20is%20connected%20to%20a%20transformer.%20%7D)
![\text { The source voltage of a transformer is }\left(V_{P}\right) \text { is } 65 \mathrm{V}](https://tex.z-dn.net/?f=%5Ctext%20%7B%20The%20source%20voltage%20of%20a%20transformer%20is%20%7D%5Cleft%28V_%7BP%7D%5Cright%29%20%5Ctext%20%7B%20is%20%7D%2065%20%5Cmathrm%7BV%7D)
![\text { The number of turns in primary winding of transformer is }\left(N_{P}\right) \text { is } 30 .](https://tex.z-dn.net/?f=%5Ctext%20%7B%20The%20number%20of%20turns%20in%20primary%20winding%20of%20transformer%20is%20%7D%5Cleft%28N_%7BP%7D%5Cright%29%20%5Ctext%20%7B%20is%20%7D%2030%20.)
We need to find the number of turns in the secondary winding
to run the bulb at 120W ![\left(P_{2}\right)](https://tex.z-dn.net/?f=%5Cleft%28P_%7B2%7D%5Cright%29)
Firstly find the secondary voltage in the transformer use, ![\frac{P_{1}}{P_{2}}=\frac{V_{1}^{2}}{V_{2}^{2}}](https://tex.z-dn.net/?f=%5Cfrac%7BP_%7B1%7D%7D%7BP_%7B2%7D%7D%3D%5Cfrac%7BV_%7B1%7D%5E%7B2%7D%7D%7BV_%7B2%7D%5E%7B2%7D%7D)
![\frac{80}{120}=\frac{120^{2}}{V_{2}^{2}}](https://tex.z-dn.net/?f=%5Cfrac%7B80%7D%7B120%7D%3D%5Cfrac%7B120%5E%7B2%7D%7D%7BV_%7B2%7D%5E%7B2%7D%7D)
![V_{2}^{2}=\frac{120^{2} \times 120}{80}](https://tex.z-dn.net/?f=V_%7B2%7D%5E%7B2%7D%3D%5Cfrac%7B120%5E%7B2%7D%20%5Ctimes%20120%7D%7B80%7D)
![V_{2}^{2}=\frac{1728000}{80}](https://tex.z-dn.net/?f=V_%7B2%7D%5E%7B2%7D%3D%5Cfrac%7B1728000%7D%7B80%7D)
![V_{2}^{2}=21600](https://tex.z-dn.net/?f=V_%7B2%7D%5E%7B2%7D%3D21600)
![V_{2}=\sqrt{21600}](https://tex.z-dn.net/?f=V_%7B2%7D%3D%5Csqrt%7B21600%7D)
![V_{2}=146.9 \mathrm{V}=V_{S}](https://tex.z-dn.net/?f=V_%7B2%7D%3D146.9%20%5Cmathrm%7BV%7D%3DV_%7BS%7D)
Now, finding the number of turns in secondary coil. Use, ![\frac{N_{P}}{N_{S}}=\frac{V_{P}}{V_{S}}](https://tex.z-dn.net/?f=%5Cfrac%7BN_%7BP%7D%7D%7BN_%7BS%7D%7D%3D%5Cfrac%7BV_%7BP%7D%7D%7BV_%7BS%7D%7D)
![\frac{30}{N_{S}}=\frac{65}{146.9}](https://tex.z-dn.net/?f=%5Cfrac%7B30%7D%7BN_%7BS%7D%7D%3D%5Cfrac%7B65%7D%7B146.9%7D)
![N_{S}=\frac{30 \times 146.9}{65}](https://tex.z-dn.net/?f=N_%7BS%7D%3D%5Cfrac%7B30%20%5Ctimes%20146.9%7D%7B65%7D)
![N_{S}=\frac{4407}{65}](https://tex.z-dn.net/?f=N_%7BS%7D%3D%5Cfrac%7B4407%7D%7B65%7D)
![N_{S}=67.8](https://tex.z-dn.net/?f=N_%7BS%7D%3D67.8)
The number of turns in the secondary winding are 67.8 turns.