Answer : C. Pascal's principle.
Explaination : Pascal's principle (well-known as Pascal's law) states that if a closed container contains a fluid at rest, then a small change in pressure at one side of the fluid is transmitted to each and every part of the fluid and also to the walls of the container without any loss. In a hydraulic lift, we need the same mechanism to work and so we take the help of Pascal's principle.
Hence, the correct option is C. Pascal's principle.
Yp(t) = A1 t^2 + A0 t + B0 t e(4t)
=> y ' = 2A1t + A0 + B0 [e^(4t) +4 te^(4t) ]
y ' = 2A1t + A0 + B0e^(4t) + 4B0 te^(4t)
=> y '' = 2A1 + 4B0e(4t) + 4B0 [ e^(4t) + 4te^(4t)
y '' = 2A1 + 4B0e^(4t) + 4B0e^(4t) + 16B0te^(4t)
Now substitute the values of y ' and y '' in the differential equation:
<span>y′′+αy′+βy=t+e^(4t)
</span> 2A1 + 4B0e^(4t) + 4B0e^(4t) + 16B0te^(4t) + α{2A1t + A0 + B0e^(4t) + 4B0 te^(4t) } + β{A1 t^2 + A0 t + B0 t e(4t)} = t + e^(4t)
Next, we equate coefficients
1) Constant terms of the left side = constant terms of the right side:
2A1+ 2αA0 = 0 ..... eq (1)
2) Coefficients of e^(4t) on both sides
8B0 + αB0 = 1 => B0 (8 + α) = 1 .... eq (2)
3) Coefficients on t
2αA1 + βA0 = 1 .... eq (3)
4) Coefficients on t^2
βA1 = 0 ....eq (4)
given that A1 ≠ 0 => β =0
5) terms on te^(4t)
16B0 + 4αB0 + βB0 = 0 => B0 (16 + 4α + β) = 0 ... eq (5)
Given that B0 ≠ 0 => 16 + 4α + β = 0
Use the value of β = 0 found previously
16 + 4α = 0 => α = - 16 / 4 = - 4.
Answer: α = - 4 and β = 0
Answer:
option (D)
Explanation:
If we plot a graph between the velocity of the object and the time taken, the slope of graph gives the value of acceleration of the object and the area under the graph gives the product of velocity and time taken that means it is displacement
Energy of an object due to the random motion of its atoms and molecules so d
Answer: 2372Kev
Eg = 2222keV
Eex = ?
Eex - Eg = 150keV
Eex - 2222 = 150
Eex = 150 + 2222
Eex = 2372keV
Explanation:
The energy possessed by the deuterium particles in their ground state or unexcited state is Eg and in that in their excited state is Eex
