Answer: 330.88 J
Explanation:
Given
Linear velocity of the ball, v = 17.1 m/s
Distance from the joint, d = 0.47 m
Moment of inertia, I = 0.5 kgm²
The rotational kinetic energy, KE(rot) of an object is given by
KE(rot) = 1/2Iw²
Also, the angular velocity is given
w = v/r
Firstly, we calculate the angular velocity. Since it's needed in calculating the Kinetic Energy
w = v/r
w = 17.1 / 0.47
w = 36.38 rad/s
Now, substituting the value of w, with the already given value of I in the equation, we have
KE(rot) = 1/2Iw²
KE(rot) = 1/2 * 0.5 * 36.38²
KE(rot) = 0.25 * 1323.5
KE(rot) = 330.88 J
Answer:
a) m_v = m_s (()² - 1) , b) m_v = 1.07 10⁻¹⁴ g
Explanation:
a) The angular velocity of a simple harmonic motion is
w² = k / m
where k is the spring constant and m is the mass of the oscillator
let's apply this expression to our case,
silicon only
w₉² =
k = w₀² m_s
silicon with virus
w² =
k = w² (m_v + m_s)
in the two expressions the constant k is the same and q as the one property of the silicon bar, let us equal
w₀² m_s = w² (m_v + m_s)
m_v = ()² m_s - m_s
m_v = m_s (()² - 1)
b) let's calculate
m_v = 2.13 10⁻¹⁶ [()² - 1)]
m_v = 1.07 10⁻¹⁴ g
Answer: d) the presence of solidified lava flows on the Moon
Explanation:
A geological activity means an occurrence of event such as volcanic eruption, earthquake, sedimentation, erosion etc. The revolution of the Moon around the Earth
, the axial tilt of the Moon or the phases of the Moon are not surface features. hence, these events cannot provide the evidence of geological activity in the past of Moon.
The surface features of moon such as Mares, Craters, mountains, Rays and rills are the proof of some geological activity on the Moon. Mares are the dark patches on the moon's surface formed of solidified lava. Due to negligible atmosphere on the moon, the meteors strike its surface and cause craters to form. Thus, the correct answer is d.
Answer:
V = 0.0723 volts = 72.3 milivolts
Explanation:
The emf induced in the rod is the motional emf due to the magnetic field. This motional emf can be calculated by the following formula:
where,
V = Motional EMF = ?
v = speed of rod = 12.5 m/s
B = Magnetic Field = 6.23 mT = 0.00623 T
l = Length of rod = 92.9 cm = 0.929 m
θ = angle between v and B = 90°
Therefore,
<u>V = 0.0723 volts = 72.3 milivolts</u>
1) In the first case, the correct answer is
<span>A.Wavelengths measured would match the actual wavelengths emitted.
In fact, the stars are not moving relative to Earth, so there is no shift in the measured wavelength.
2) In this second case, the correct answer is
</span><span>A.Wavelengths measured would be shorter than the actual wavelengths emitted.
</span>in fact, since the stars in this case are moving towards the Earth, then apparent frequency of their emitted light will be larger than the actual frequency, because of the Doppler effect, according to the formula:
where f0 is the actual frequency, f' the apparent frequency, c the speed of light and vs the velocity of the source (the stars) relative to the obsever (Earth). Vs is negative when the source is moving towards the observer, so the apparent frequency f' is larger than the actual frequency f0. But the wavelength is inversely proportional to the frequency, so the apparent wavelength will be shorter than the actual wavelength.