The correct option is 0.5 M
Calculation
Wavelength is defined as the ratio of velocity of a wave to its frequency. It is measure in meters. Mathematically, wavelength is given by the following formula:
Wavelength = wave velocity / frequency
From the details given in the question,
Wavelength =?
Velocity = 340 m/s
Frequency = 680 HZ
Wavelength = 340 /680 = 0.5
Therefore, wavelength = 0.5 M
Answer:
Explanation:
Let the tension in the cord be T₁ and T₂ .
for motion of block placed on horizontal table
T₁ = m a , a is acceleration of the whole system .
for motion of hanging bucket of mass m
mg - T₂ = ma
adding the two equation
mg + T₁- T₂ = 2ma
for rotational motion of the pulley
torque = moment of inertia x angular acceleration
(T₂ - T₁) R = I x α , I is moment of inertia of pulley , α is angular acceleration .
(mg - 2ma ) R = I x α
(mg - 2ma ) R = I x a / R
(mg - 2ma ) R² = I x a
mgR² = 2ma R² + I x a
a = mgR² / (2m R² + I )
Since body moves by distance d in time T
d = 1/2 a T²
a = 2d / T²
mgR² / (2m R² + I ) = 2d / T²
mgR²T² = 2d x (2m R² + I )
mgR²T² - 4dm R² = 2dI
m R² ( gT² - 4d ) = 2dI
I = m R² ( gT² - 4d ) ] / 2d .
Answer:
The two objects will collide with the same position vector for all three components at exactly t = 4 s
Explanation:
For two particles starting out at the same time to collide, their position Vector's at the time of collision must be exactly the same.
So, at the collision point, position vector of object 1 is equated to that of object 2.
r₁ = (t², 13t-36, t²)
r₂ = (7t-12, t², 5t-4)
At he point of collision
t² = 7t - 12
t² - 7t + 12 = 0
t² - 4t - 3t + 12 = 0
t(t - 4) - 3(t - 4) = 0
t = 3s or t = 4s
13t - 36 = t²
t² - 13t + 36 = 0
t² - 4t - 9t + 36 = 0
t(t - 4) - 9(t - 4) = 0
t = 9s or 4s
t² = 5t - 4
t² - 5t + 4 = 0
t² - 4t - t + 4 = 0
t(t - 4) - 1(t - 4) = 0
t = 1s or t = 4s
The three components intersect at other times, but at t = 4s, they all intersect at the same time! Meaning that, at this point the two objects are at the same place with the same position vector at that time.
Answer:
The point at which the electrical potential is zero is x = +0.33 m.
Explanation:
By definition the electrical potential is:
Where:
K: is Coulomb's constant = 9x10⁹ N*m²/C²
q: is the charge
r: is the distance
The point at which the electrical potential is zero can be calculated as follows:
(1)
q₁ is the first charge = +3 mC
r₁ is the distance from the point to the first charge
q₂ is the first charge = -6 mC
r₂ is the distance from the point to the second charge
By replacing r₁ = 1 - r₂ into equation (1) we have:
(2)
By solving equation (2) for r₂:
Therefore, the point at which the electrical potential is zero is x = +0.33 m.
I hope it helps you!
Answer: 183.8Hz
Explanation:
Given that,
wavelength of sound (λ) = 1.85 m
frequency of the sound (F) = ?
Recall that the speed of sound (V) in air is a constant with a value of 340m/s
So, apply the formula
V = F λ
340 m/s = F x 1.85 m
F = 340m/s / 1.85m
F = 183.8Hz
Thus, the frequency of the sound that is
generated is 183.8 hertz
