Answer:
F = GMmx/[√(a² + x²)]³
Explanation:
The force dF on the mass element dm of the ring due to the sphere of mass, m at a distance L from the mass element is
dF = GmdM/L²
Since the ring is symmetrical, the vertical components of this force cancel out leaving the horizontal components to add.
So, the horizontal components add from two symmetrically opposite mass elements dM,
Thus, the horizontal component of the force is
dF' = dFcosФ where Ф is the angle between L and the x axis
dF' = GmdMcosФ/L²
L² = a² + x² where a = radius of ring and x = distance of axis of ring from sphere.
L = √(a² + x²)
cosФ = x/L
dF' = GmdMcosФ/L²
dF' = GmdMx/L³
dF' = GmdMx/[√(a² + x²)]³
Integrating both sides we have
∫dF' = ∫GmdMx/[√(a² + x²)]³
∫dF' = Gm∫dMx/[√(a² + x²)]³ ∫dM = M
F = GmMx/[√(a² + x²)]³
F = GMmx/[√(a² + x²)]³
So, the force due to the sphere of mass m is
F = GMmx/[√(a² + x²)]³
Answer:
<h3>473.8 m/s; 473.8 m/s</h3>
Explanation:
Given the initial velocity U = 670m/s
Horizontal velocity Ux = Ucos theta
Vertical component of the cannon velocity Uy = Usin theta
Given
U = 670m/s
theta = 45°
horizontal component of the cannonball’s velocity = 670 cos 45
horizontal component of the cannonball’s velocity = 670(0.7071)
horizontal component of the cannonball’s velocity = 473.757m/s
Vertical component of the cannonball’s velocity = 670 sin 45
Vertical component of the cannonball’s velocity = 670 (0.7071)
Vertical component of the cannonball’s velocity = 473.757m/s
Hence pair of answer is 473.8 m/s; 473.8 m/s
Answer:
ya we can write the imaginary character's name .
So that we can identify these imaginary people, as we cannot simply write the conversation and leave it .
Or maybe sometimes the reader will get confused as there is no name for the two people .
So, i suggest that you should write the names
Explanation:
You can even ask to your class teacher for further clarification
Answer: The correct answer for the blank is -
C. closure.
Gestalt principle of closure describes how we perceive complete figures even when the information that form the figure is missing.
This is due the fact that our brain responds to the familiar patterns inspite of getting incomplete information.
For instance, in the given question, we are able to perceive an image of square in the center despite not having actual lines that form a square.
Thus, it represents principle of closure.
Answer:
C: Variation in the value of g as the pendulum bob moves along its arc.
Explanation:
The formula for period of a simple pendulum is given by;
T = 2π√(L/g)
Where;
L is length
g is acceleration due to gravity
Now, from this period equation, it is clear that the only thing that can affect the period of a simple pendulum are changes to its length and acceleration due to gravity.
Looking at the options, the only one that talks about either the length or gravity as being potential causes of the error is option C
