Bode's Law: correctly predicted the location of Jupiter, uses a number sequence to determine planetary distances, incorrectly pr
1 answer:
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Answer:
T0=390 degF
Explanation:
The thermometer reading 70◦Fis placed in an oven preheated to a constant temperature. Through the glass window in the oven door, an observer records that the thermometer reads 110◦F after 12 minutes and 145◦F after 1 minute. How hot is the oven? Newton’s law of cooling yields the following differential equationdTdt=k(T−T0), whereT0 is the ambient temperature.
If T is temperature, then by Newton’s law
dTdt=-k(T−T0)
Where
T0− is temperature of oven
∫
ln(T-T0), from 110 to 70=-kt, from 1/2 to 0
ln(110-T0)-ln(70-T0)=-k(1/2-0)
integrating the LHS of the equation from 110 to 145F
∫∫∫
ln(145-T0)-ln(110-T0)=-k(1-1/2)
2ln145-T0/(110-T0)=-k
k=-2lnT0-145/(T0-110).......................2
couplijng equatiuon 2 with 1
(T0-110)^2=(T0-70)(T0-145)
T0^2-220T0+12100=T0^2-215T0+10150
5T0=1950
T0=390 degF
Answer:
The period would decrease by sqrt(2)
Explanation:
The restoring force is given by,
F = -kx
According to Newton's second law of motion,
ma = -kx
ma + kx = 0
The time period is given by,
T =
Where is the angular velocity and it is given by,
=
Now if the spring constant is doubled then,
Thus,
=
Thus, The period would decrease by sqrt(2).
Hence, option D is correct.
Answer:
1.196 μm
Explanation:
D = Screen distance = 3 m
= Wavelength = 598 m
y = Distance of first-order bright fringe from the center of the central bright fringe = 4.84 mm
d = Slit distance
For first dark fringe
Wavelength of first-order dark fringe observed at this same point on the screen is 1.196 μm