Answer:
d) 1000 times
Explanation:
As we know that difference of sound level is given as
![L_2 - L_1 = 10 Log \frac{I_2}{I_1}](https://tex.z-dn.net/?f=L_2%20-%20L_1%20%3D%2010%20Log%20%5Cfrac%7BI_2%7D%7BI_1%7D)
so here we need to find the ratio of two intensity
it is given as
![Log\frac{I_2}{I_1} = \frac{(L_2- L_1)}{10}](https://tex.z-dn.net/?f=Log%5Cfrac%7BI_2%7D%7BI_1%7D%20%3D%20%5Cfrac%7B%28L_2-%20L_1%29%7D%7B10%7D)
![Log\frac{I_2}{I_1} = \frac{60 - 30}{10}](https://tex.z-dn.net/?f=Log%5Cfrac%7BI_2%7D%7BI_1%7D%20%3D%20%5Cfrac%7B60%20-%2030%7D%7B10%7D)
![Log\frac{I_2}{I_1} = 3](https://tex.z-dn.net/?f=Log%5Cfrac%7BI_2%7D%7BI_1%7D%20%3D%203)
now we have
![\frac{I_2}{I_1} = 10^3](https://tex.z-dn.net/?f=%5Cfrac%7BI_2%7D%7BI_1%7D%20%3D%2010%5E3)
so it is
d) 1000 times
Momentum, p = m.v
m of the girl = 60.0 kg
m of the boat = 180 kg
v of the girl = 4.0 m/s
A) Momentum of the girl as she is diving:
p = m.v = 60.0 kg * 4.0 m/s = 24.0 N/s
B) momentum of the raft = - momentum of the girl = -24.0 N/s
C) speed of the raft
p = m.v ; v = p/m = 24.0N/s / 180 kg = -0.13 m/s [i.e. in the opposite direction of the girl's velocity]
Explanation:
https://educationalghana.news.blog/2021/08/09/geography-human-physical-and-practical-for-wassce-novdec-candidates/
Answer:
![\frac{\dot Q}{A} =20.129\ W.m^{-2}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cdot%20Q%7D%7BA%7D%20%3D20.129%5C%20W.m%5E%7B-2%7D)
& ![T_2=2.41875\ ^{\circ}C](https://tex.z-dn.net/?f=T_2%3D2.41875%5C%20%5E%7B%5Ccirc%7DC)
Explanation:
Given:
- interior temperature of box,
![T_i=30^{\circ}C](https://tex.z-dn.net/?f=T_i%3D30%5E%7B%5Ccirc%7DC)
- height of the walls of box,
![h=3\ m](https://tex.z-dn.net/?f=h%3D3%5C%20m)
- thickness of each layer of bi-layered plywood,
![x_p=1.25\ cm=0.0125\ m](https://tex.z-dn.net/?f=x_p%3D1.25%5C%20cm%3D0.0125%5C%20m)
- thermal conductivity of plywood,
![k_p=0.104\ W.m^{-1}.K^{-1}](https://tex.z-dn.net/?f=k_p%3D0.104%5C%20W.m%5E%7B-1%7D.K%5E%7B-1%7D)
- thickness of sandwiched Styrofoam,
![x_s=5\ cm=0.05\ m](https://tex.z-dn.net/?f=x_s%3D5%5C%20cm%3D0.05%5C%20m)
- thermal conductivity of Styrofoam,
![k_s=0.04\ W.m^{-1}.K^{-1}](https://tex.z-dn.net/?f=k_s%3D0.04%5C%20W.m%5E%7B-1%7D.K%5E%7B-1%7D)
- exterior temperature,
![T_o=0^{\circ}C](https://tex.z-dn.net/?f=T_o%3D0%5E%7B%5Ccirc%7DC)
<u>From the Fourier's law of conduction:</u>
![\dot Q=\frac{dT}{(\frac{x}{kA}) }](https://tex.z-dn.net/?f=%5Cdot%20Q%3D%5Cfrac%7BdT%7D%7B%28%5Cfrac%7Bx%7D%7BkA%7D%29%20%7D)
....................................(1)
<u>Now calculating the equivalent thermal resistance for conductivity using electrical analogy:</u>
![R_{th}=R_p+R_s+R_p](https://tex.z-dn.net/?f=R_%7Bth%7D%3DR_p%2BR_s%2BR_p)
![R_{th}=\frac{x_p}{k_p.A}+\frac{x_s}{k_s.A}+\frac{x_p}{k_p.A}](https://tex.z-dn.net/?f=R_%7Bth%7D%3D%5Cfrac%7Bx_p%7D%7Bk_p.A%7D%2B%5Cfrac%7Bx_s%7D%7Bk_s.A%7D%2B%5Cfrac%7Bx_p%7D%7Bk_p.A%7D)
![R_{th}=\frac{1}{A} (\frac{x_p}{k_p}+\frac{x_s}{k_s}+\frac{x_p}{k_p})](https://tex.z-dn.net/?f=R_%7Bth%7D%3D%5Cfrac%7B1%7D%7BA%7D%20%28%5Cfrac%7Bx_p%7D%7Bk_p%7D%2B%5Cfrac%7Bx_s%7D%7Bk_s%7D%2B%5Cfrac%7Bx_p%7D%7Bk_p%7D%29)
![R_{th}=\frac{1}{A} (\frac{0.0125}{0.104}+\frac{0.05}{0.04}+\frac{0.0125}{0.104})](https://tex.z-dn.net/?f=R_%7Bth%7D%3D%5Cfrac%7B1%7D%7BA%7D%20%28%5Cfrac%7B0.0125%7D%7B0.104%7D%2B%5Cfrac%7B0.05%7D%7B0.04%7D%2B%5Cfrac%7B0.0125%7D%7B0.104%7D%29)
.....................(2)
Putting the value from (2) into (1):
![\dot Q=\frac{30-0}{\frac{1.4904}{A} }](https://tex.z-dn.net/?f=%5Cdot%20Q%3D%5Cfrac%7B30-0%7D%7B%5Cfrac%7B1.4904%7D%7BA%7D%20%7D)
![\dot Q=\frac{30\ A}{1.4904}](https://tex.z-dn.net/?f=%5Cdot%20Q%3D%5Cfrac%7B30%5C%20A%7D%7B1.4904%7D)
is the heat per unit area of the wall.
The heat flux remains constant because the area is constant.
<u>For plywood-Styrofoam interface from inside:</u>
![\frac{\dot Q}{A} =k_p.\frac{T_i-T_1}{x_p}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cdot%20Q%7D%7BA%7D%20%3Dk_p.%5Cfrac%7BT_i-T_1%7D%7Bx_p%7D)
![20.129=0.104\times \frac{30-T_1}{0.0125}](https://tex.z-dn.net/?f=%2020.129%3D0.104%5Ctimes%20%5Cfrac%7B30-T_1%7D%7B0.0125%7D)
![T_1=27.58\ ^{\circ}C](https://tex.z-dn.net/?f=T_1%3D27.58%5C%20%5E%7B%5Ccirc%7DC)
&<u>For Styrofoam-plywood interface from inside:</u>
![\frac{\dot Q}{A} =k_s.\frac{T_1-T_2}{x_s}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cdot%20Q%7D%7BA%7D%20%3Dk_s.%5Cfrac%7BT_1-T_2%7D%7Bx_s%7D)
![20.129=0.04\times \frac{27.58-T_2}{0.05}](https://tex.z-dn.net/?f=%2020.129%3D0.04%5Ctimes%20%5Cfrac%7B27.58-T_2%7D%7B0.05%7D)
![T_2=2.41875\ ^{\circ}C](https://tex.z-dn.net/?f=T_2%3D2.41875%5C%20%5E%7B%5Ccirc%7DC)
Answer:
a) 1450watts
b) 564watts
c) 1.11
Explanation:
Power consumed = IV
I is the current rating
V is the operating voltage
If a blow-dryer and a vacuum cleaner each operate with a voltage of 120 V and the current rating of the blow-dryer is 12 A, while that of the vacuum cleaner is 4.7 A then their individual power rating is calculated thus;
a) For blow-dryer
Operating voltage = 120V
Its current rating = 12A
Power consumed = IV
= 120×12
= 1440watts
b) For vacuum cleaner:
Operating voltage is the same as that of blow dryer = 120V
Its current rating = 4.7A
Power consumed = IV
= 120×4.7
= 564watts
c) Energy used = Power consumed × time taken
Energy used = Power × time
Energy used by blow dryer = 1440×20×60
= 1,728,000Joules
Energy used up by vacuum cleaner = 564×46×60
= 564×2760
= 1,556,640Joules
Ratio of the energy used by the blow-dryer in 20 minutes to the energy used by the vacuum cleaner in 46 minutes will be 1,728,000/1,556,640 = 1.11