Answer:
2/7 I
Explanation:
The theorem of parallel axis states that the moment of inertia of a body about a certain axis z' is equal to the moment of inertia of the body about the axis passing through the centre, z, plus the product between the mass of the body (M) and the square of the distance (r) between the two axis:
[tex]I_z' = I_z + Mr^2[/tex] (1)
For a solid sphere, the moment of inertia about the axis passing through the centre is
[tex]I_z=\frac{2}{5}MR^2[/tex] (2)
where R is the radius of the sphere.
The moment of inertia about an axis tangent to the surface then will be (applying (1) using r=R):
[tex]I = \frac{2}{5}MR^2 + MR^2 = \frac{7}{5}MR^2[/tex] (3)
The problem asks us to rewrite [tex]I_z[/tex], the moment of inertia about the centre, in terms of I, the moment of inertia about the axis tangent to the surface. We can do it by rewriting (2) as follows:
[tex]MR^2 = \frac{5}{2}I_z[/tex]
And substituting this into (3):
[tex]I=\frac{7}{5}(MR^2 )=\frac{7}{5}(\frac{5}{2} I_z) = \frac{7}{2}I_z\\I_z = \frac{2}{7}I[/tex]
The moment of inertia of a uniform solid sphere about an axis through its center is 3/5 times the moment of inertia of the sphere about an axis tangent to its surface. This is calculated using the parallel axis theorem.
The correct option is b.
Explanation:In physics, the moment of inertia of a sphere about an axis through its center is determined using the parallel axis theorem. The formula of the parallel axis theorem is: Icm = I + Mh2, where Icm is the moment of inertia about an axis through the center of mass, I is the moment of inertia about a parallel axis through the edge of the sphere, M is the mass of the sphere, and h is the distance between the two axes.
In this case, the sphere is uniform, so its center of mass is in its geometric center. The axis through the edge of the sphere is a distance of the radius of the sphere away from the axis through its center, so h = r. Also, in a solid sphere, the moment of inertia, Icm, about an axis through its center is (2/5)MR2.
With these values substituted into the formula, we have: (2/5)MR2 = I + MR2.
From this it can be deduced that I = 2/5 MR2 - MR2 = -(3/5) MR2. So the moment of inertia of this sphere about an axis through its center is (3/5) times smaller than the moment of inertia about an axis tangent to its surface.
This gives us an answer of choice b) 3/5 I.
Learn more about Moment of Inertia here:https://brainly.com/question/30051108
#SPJ3
A nuclear weapon in which enormous energy is released
A car moves at a constant speed of 10 m/s. If the car doesn't accelerate during the next 40 s how far will it go?
A) 200 m
B) 400 m
C) 50 m
D) 0.25 m
the answer is b. space = time * velocity
The distance travelled by the car will be 400 m. Option B is correct.
What is distance?Distance is a numerical representation of the distance between two objects or locations.
Distance can refer to a physical length or an estimate based on other factors in physics or common use. |AB| is a symbol for the distance between two points A and B.
Given data;
Speed (V)= 10 m/s.
Time (t)=40 s
The distance travelled by the car will be;
Distance = speed × time
Distance =10 m/s × 40 s
Distance =400 m
The distance travelled by the car will be 400 m.
Hence,option B is correct.
To learn more about the distance refer to the link;
https://brainly.com/question/26711747
#SPJ2
Why do most earthquakes occur at tectonic plate boundaries
Answer:
Notice that many plate boundaries do not coincide with coastlines. Earthquakes can also occur far from the edges of plates, along faults. Faults are cracks in the earth where sections of a plate (or two plates) are moving in different directions. Faults are caused by all that bumping and sliding the plates do.
The volume of a gas is reduced from 4 l to 0.5 l while the temperature is held constant. How does the gas pressure change?
Answer:
The pressure increases by a factor 8
Explanation:
For a gas held at constant temperature, Boyle's law can be applied. It states that the product of the gas pressure and the gas volume is constant, so we can write:
[tex]p_1 V_1 = p_2 V_2[/tex]
where
[tex]p_1[/tex] is the initial pressure
[tex]p_2[/tex] is the final pressure
[tex]V_1[/tex] is the initial volume
[tex]V_2[/tex] is the final volume
For the gas in this problem, the volume is reduced from
[tex]V_1 = 4 L[/tex]
to
[tex]V_2 = 0.5 L[/tex]
so we can rewrite the equation as
[tex]\frac{p_2}{p_1}=\frac{V_1}{V_2}=\frac{4 L}{0.5 L}=8[/tex]
this means that the pressure of the gas will increase by a factor 8.
A thin rod of length 1.3 m and mass 250 g is suspended freely from one end. It is pulled to one side and then allowed to swing like a pendulum, passing through its lowest position with angular speed 5.88 rad/s. Neglecting friction and air resistance, find (a) the rod's kinetic energy at its lowest position and (b) how far above that position the center of mass rises. (a) Number Enter your answer for part (a) in accordance to the question statement Units Choose the answer for part (a) from the menu in accordance to the question statement
(a) 2.42 J
The kinetic energy of a rotating object is given by:
[tex]K=\frac{1}{2}I \omega^2[/tex]
where
I is the moment of inertia
[tex]\omega[/tex] is the angular speed
Here we have
[tex]\omega=5.88 rad/s[/tex] at the lowest point of the trajectory
While the moment of inertia of a rod rotating around one end is
[tex]I=\frac{1}{3}ML^2 = \frac{1}{3}(0.250 kg)(1.3 m)^2=0.14 kg m^2[/tex]
And substituting in the previous formula, we find the kinetic energy at the lowest position:
[tex]K=\frac{1}{2}(0.14 kg m^2)(5.88 rad/s)^2=2.42 J[/tex]
(b) 0.99 m
According to the law of conservation of energy, the total mechanical energy (sum of kinetic energy and potential energy) must be conserved:
[tex]E=K+U[/tex]
At the lowest point, we can take the potential energy as zero, so the mechanical energy is just kinetic energy:
[tex]E=K=2.42 J[/tex]
At the highest point in the trajectory, the rod is stationary, so the kinetic energy will be zero, and the mechanical energy will simply be equal to the gravitational potential energy:
[tex]E=2.42 J = U = mgh[/tex]
where h is the heigth of the centre of mass of the rod with respect to the lowest point of the trajectory. Solving for h, we find
[tex]h=\frac{E}{mg}=\frac{2.42 J}{(0.250 kg)(9.81 m/s^2)}=0.99 m[/tex]
A dolphin jumps out of the water. As it falls back down it a clerated at a rate of -9,8m/s^2 for 0.8 seconds of free fall. To calculate how far the dolphin fell, what equation will you use?
Answer:
0.196 m
Explanation:
Given in the question that,
time taken by the dolphin to go back to water = 0.2 sec
To solve the question we will use Newton's Law of motion
S = ut + 0.5(a)t²here S is distance covered
u is initial speed
a = acceleration due to gravity
t = time taken
Plug value in the equation above
S = 0(0.2) + 0.5(-9.8)(0.2)²
S = 0.5(-9.8)(0.2)²
S = -0.196 m
Negative sign represent direction
(Assuming that dolphin have a vertical straight jump not a projectile motion)
every magnetic has ____ unlike poles
Has two unlike poles
2
Take for example the Earth, which has two magnetic poles: one in the north and one in the south.
A collision between two large spiral galaxies is likely to produce
A large elliptical galaxy. Hope this helped
Final answer:
A collision between two spiral galaxies generally results in the creation of a single elliptical galaxy, involving gravitational interactions and often triggering new star formation. Through observations and simulations, we see this process unfold over very long time scales.
Explanation:
A collision between two large spiral galaxies is likely to result in the formation of a single, more massive elliptical galaxy. During such a collision, which is more accurately described as a 'merger', the gravitational forces between the stars and dark matter in each galaxy cause them to interact. While individual stars do not physically collide due to vast interstellar distances, the gas components of the galaxies can collide and trigger bursts of new star formation. This process can also give rise to phenomena such as starburst galaxies and active galactic nuclei (AGN), which can have a significant impact on the evolution of galaxies.
Galactic collisions are intricate, slow-moving interactions happening over timescales of hundreds of millions to a billion years. Through Hubble Space Telescope observations and computer simulations, we have been able to witness these awe-inspiring events, which provide insight into how galaxies evolve. For example, in a computer simulation of a collision between two spiral galaxies, one can see the transformation unfolding where two separate spirals gradually merge to form a single elliptical galaxy, marked by extensive star formation.
A simple pendulum consists of a point mass suspended by a weightless, rigid wire in a uniform gravitation field. Which of the following statements are true when the system undergoes small oscillations?Check all that apply.The period is inversely proportional to the suspended mass.The period is proportional to the square root of the length of the wire.The period is independent of the suspended mass.The period is proportional to the suspended mass.The period is independent of the length of the wire.The period is inversely proportional to the length of the wire.
Answer:
The period is proportional to the square root of the length of the wire.
The period is independent of the suspended mass.
Explanation:
The period of a simple pendulum, in the small angle oscillation approximation, is given by
[tex]T=2\pi \sqrt{\frac{L}{g}}[/tex]
where
L is the length of the pendulum
g is the acceleration due to gravity
From the formula, we notice the following facts:
- The period is proportional to the square root of the length of the wire, L
- The period is independent of the suspended mass, m
So, these are the two correct statements.
For which optical devices does d sometimes have a positive value
Answer:
B) A & C
Explanation:
Determine the empirical formula of a compound containing 83% potassium and 17.0% oxygen.
The empirical formula of the compound containing 83% potassium and 17.0% oxygen is K2O.
Explanation:To determine the empirical formula of a compound containing 83% potassium and 17.0% oxygen, we need to convert these percentages into moles. Assuming we have 100g of the compound, we can calculate the moles of potassium and oxygen. The molar mass of potassium is 39.10 g/mol and the molar mass of oxygen is 16.00 g/mol.
So, the moles of potassium is 83g / 39.10 g/mol = 2.12 mol and the moles of oxygen is 17g / 16.00 g/mol = 1.06 mol.
Next, we divide the moles of each element by the smallest number of moles to get the simplest whole number ratio. In this case, the ratio is approximately 2 K: 1 O. Therefore, the empirical formula of the compound is K2O.
Learn more about Empirical Formula here:https://brainly.com/question/32125056
#SPJ3
Planet with the most extreme temperature range
Mercury.
On the side that is facing sun it's extremely hot.
On the other side it's extremely cold.
Hope this helps.
r3t40
Andrew has a four-year college loan for $20,000. The lender charges a simple interest rate of 5 percent. How much interest will he have to pay? simple interest = P × r × t A. $800 B. $4,000 C. $10,000
Answer:
B. $4,000
Explanation:
The formula for the simple interest is
[tex]interest = P\cdot r \cdot t[/tex]
where
P is the principal
r is the interest rate
t is the number of years
In this problem,
P = 20,000 $
r = 0.05
t = 4 years
So the interest is
[tex]P=(20,000 $)(0.05 )(4)=4,000 $[/tex]
What is the minimum eccentricity an ellipse can have
Answer:
Zero (the ellipse is a circle)
Explanation:
The eccentricity of an ellipse is defined as the ratio between the distance of each focus from the centre of the ellipse (c) and the length of the semimajor axis (a):
[tex]e = \frac{c}{a}[/tex]
For a perfect circle, the focii correspond to the centre of the circle, so
c = 0
which means that for a circle,
e = 0
Therefore, the minimum value of the eccentricity of an ellipse is zero, and it occurs when the ellipse coincides with a circle.
In a displacement versus time graph, what does the slope of a line at any point indicate?
acceleration
maximum displacement
minimum displacement
velocity
In a displacement versus time graph, the slope of the line at any point on the graph indicates the magnitude of velocity.
(It can't indicate velocity completely, because the graph shows nothing about the direction of the motion.)
In a displacement versus time graph, the slope of the line at any point on the graph indicates the magnitude of velocity.
What is velocity?Velocity is the time rate of change of displacement. The displacement and velocity both are vector quantities. They represent magnitude and direction as well.
velocity = change in displacement / change in time
v = ds/dt
So, the slope of line showing the graph of displacement vs time give s an idea of velocity of the particle.
Thus, the slope of the line at any point on the graph indicates the magnitude of velocity.
Learn more about velocity.
https://brainly.com/question/14501665
#SPJ2
Mechanical energy is conserved in the presence of which of the following types of forces?Select all that apply. A- electrostatic B- frictional C- magnetic D- gravitational
Mechanical energy remains constant (conserved) if only conservative forces act on the particles.
In this sense, the following forces are conservative:
-Gravitational
-Elastic
-Electrostatics
While the Friction Force and the Magnetic Force are not.
According to this, mechanical energy is conserved in the presence of electrostatic and gravitational forces. Therefore the correct options are A and D.
Answer:
A- electrostatic
C- magnetic
D- gravitational
Explanation:
As per mechanical energy conservation law we can say that when all conservative forces are present on the system then mechanical energy is always conserved
So here we have to choose all such options which will give conservative forces only
so correct answers are
A- electrostatic
C- magnetic
D- gravitational
What name is given to the rate at which energy is transferred?
Answer:
Power
Explanation:
By definition, power is the rate of energy transfer from one system to another. It is measured in Watts or Joule per second. Power can also be defined as the rate work is done. It can also be calculated using the formula:
[tex]Power = \dfrac{Work}{Time}[/tex]
Power is the name given to the rate at which energy is transferred, and it's a fundamental concept in physics related to work and heat transfer.
Explanation:The name given to the rate at which energy is transferred is called power. This concept is central in the field of physics, especially when discussing mechanical or electrical systems where energy transfer can occur at varying rates. For example, when an external force is exerted on an object that causes it to move through a distance, the energy transferred in the process is known as work. The power of a system defines how quickly this work is done or how rapidly energy is transferred into, out of, or within the system.
The rate of heat transfer by emitted radiation can be described by the Stefan-Boltzmann law, which incorporates the surface area, temperature, and the Stefan-Boltzmann constant to calculate power. Common units of energy used in such calculations include the kilocalorie (kcal) and the joule (J).
A sample of iron has a volume of 10.0 mL. The density of iron is 7.87 g/mL. Which is the correct expression to calculate the mass of the sample using dimensional analysis? a. 10.0 mL x (7.87 g / 1 mL) b. 10.0 mL x (1 g / 7.87 mL) c. 10.0 mL x (1 mL / 7.87 g) d. 10.0 mL x (7.87 mL / 1 g)
Answer:
a. 10.0 mL x (7.87 g / 1 mL)
Explanation:
Mass is density times volume. Therefore:
m = 10.0 mL x (7.87 g / 1 mL)
A string on a harp supports a wave with a wavelength of 2.4 m and a frequency of 215.0 Hz. Calculate the wave speed.
The wave speed will be 516 m/sec. The wave speed is the product of the wavelength and the frequency of the wave.
What is wavelength?The distance between two successive troughs or crests is known as the wavelength. The peak of the wave is the highest point, while the trough is the lowest.
The wavelength is also defined as the distance between two locations in a wave that have the same oscillation phase.
The given data in the problem is;
v is the speed = ?
f is the frequency= 215.0 Hz.
λ is the wavelength of the wave= 2.4 m
The relationship between the wave's wavelength, frequency, and speed is given as;
wavelength = speed of wave / frequency
The speed of the wave is found as;
[tex]\rm \lambda= \frac{v}{f} \\\\ \rm v = \lambda \times f \\\\\ \rm v = 2.4 \times 215 \\\\ v= 516 \ m/sec[/tex]
Hence, the wave speed will be 516 m/sec.
To learn more about the wavelength, refer to the link;
brainly.com/question/7143261
#SPJ2
When current is flowing in an ordinary metal wire, the magnitude of the average velocity of the electrons is closest toa) 10 m/sb) the speed of lightc) 10 microns/sd) 1 km/se) 1 m/s
Answer:
c) 10 microns/s
Explanation:
The drift velocity (the velocity of the current) of the electrons in a wire is given by
[tex]v=\frac{I}{nAq}[/tex]
where
I is the current
n is the electron number density (the number of electrons per unit volume)
A is the cross-sectional area of the wire
[tex]q=1.6\cdot 10^{-19} C[/tex] is the charge of one electron
Taking a current of
I = 1 A
in a wire of radius r = 1 mm (0.001 m), so with cross-sectional area
[tex]A=\pi r^2 = \pi (0.001 m)^2=3.14\cdot 10^{-6} m^2[/tex]
made of copper, whose electron density number is around
[tex]n=8.5\cdot 10^{28} m^{-3}[/tex]
we find
[tex]v=\frac{1 A}{(8.5\cdot 10^{28} m^{-3})(3.14\cdot 10^{-6} m^2)(1.6\cdot 10^{-19} C)}=2.34\cdot 10^{-5} m/s[/tex]
which means that the closest estimate is
c) 10 microns/s
A wire carries a 2a current. what is the current in a second wire that delivers twice as much charge in the same amount of time?
Answer:
4A
Explanation:
Current is charge per time. So if the second wire delivers twice as much charge in the same amount of time, it must have twice the current.
2 × 2A = 4A
The current in the second wire that delivers twice as much charge in the same amount of time is 4 amperes (4A).
How to determine the currentCurrent is defined as the rate of flow of electric charge, so if the first wire carries a 2A current, it delivers 2 coulombs of charge per second (1 A = 1 C/s).
To deliver twice as much charge in the same time, the second wire must deliver 4 coulombs of charge per second.
Therefore, its current is 4 amperes (4A) because it delivers 4C of charge per second, which is double the charge delivered by the first wire.
Learn about current at: https://brainly.com/question/1100341
#SPJ3
Maria drove to the store and then to work.
What is Maria's total displacement during her trip?
A) 0 km
B) 30 km
C) 60 km
D) 65 km
Answer: C - 60km !!!
Explanation:
What is the best way to support your hypothesis
Answer:
Making a Hypothesis
Explanation:
-Research the subject of your question. Review the literature and find out as much as you can about previous information and discoveries surrounding your question.
-Develop an educated guess that answers your initial question. This is your hypothesis. Make a prediction based on your hypothesis and state it as a cause-effect relationship.
In order to move a box filled with equipment to the second story loft in the warehouse, several students built a ramp or inclined plane. There was some disagreement on the height and material for the ramp. The loft height was 2.5 meters. Sara suggested a very long ramp, approximately 25 meters long. The other students disagreed, insisting it would take too much effort to push the box that distance and the ramp should be much shorter and steeper. Instead they built a ramp 10 meters in length. What comments would you make to the students based solely on the mechanical advantage of an inclined plane?
Answer:
A. sara is correct. IMA = length/height
Explanation:
Answer:
The longer the ramp, the greater the AMA.
Explanation:
When you are creating devices, mechanical devices like ramps to make a job easier for the human being, you want to create them as efficient and with the most upside possible, in that case when building a ramp the longer the ramp the easier it is to push something upwards on it, because the weight of the object is less taken into consideration as the angle of the ramp becomes smaller.
Forces that are equal in size but opposite in direction are
Answer:
Balanced Forces
Explanation:
Balanced forces do not cause a change in the motion of objects. Forces that cause a change in motion of objects are called unbalanced forces. Unbalanced forces can change the motion of an object in two ways.
Forces that are equal in size but opposite in direction are called balanced forces. Balanced forces do not cause a change in the motion of objects. Forces that cause a change in motion of objects are called unbalanced forces. Unbalanced forces can change the motion of an object in two ways.
What is/are responsible for creating variations in climate and weather at different latitudes?
A. Nothing-climate and weather aren't different at different latitudes
B. Microclimates at different latitudes
C. Different levels of sunlight at different latitudes
D. El Niño Southern Oscillation
Answer:
C. Different levels of sunlight at different latitudes
Explanation:
If we take the arrangement of the climate types on Earth, we can easily notice that they are arranged roughly by latitude. The tropical climates are in the lower latitudes, the temperature climates are in the mid-latitudes, while the polar climates are in the high latitudes. The reason for this is that the sunlight doesn't heat every part of the Earth equally. The low latitudes are receiving sunlight at a direct or close to direct angle, thus the sunlight is more concentrated and they are warm.hot all year round. Because of the tilting of the Earth, and because of the rounded shape of it, the sunlight falls at smaller angle in the mid-latitudes, with changes of the angle of fall throughout the year, so there's seasons with drastically different weather conditions. The high latitudes receive sunlight at a very low angle, resulting in dispersal of the sunlight on much greater area, thus heating up the surface very little,. resulting in very cold weather conditions.
the shopping cart is moving forward. What force moves it forward?
The force of the man pushing on the handle.
The force of the wheels pushing on the floor.
The force of the floor pushing on the wheels.
The weight of the shopping cart supplied by gravity.
Answer:
The force of the man pushing on the handle
Explanation:
The man pushing the cart is the main and only way the cart will move. If he didn't push it, he cart would just come to a halt....
It's A, The force of the man pushing on the handle
Which of the following is the hottest part of the sun?
Convective zone
Inner core
Photosphere
Radiative zone
Answer:
Inner core
Explanation:
The hottest layer of the sun is its core
The hottest part of the sun in the solar system is the Inner core.
What is sun?Sun can be regarded as one of the star which is found around Earth.
This sun is part of the components of the solar system , and it consists of different layers such as the inner part which is the hottest as well as the radiative zone.
Therefore, the temperature of the inner core of the sun is approximately 27 million degrees F, which made it hotter than Photosphere as well as Convective zone.
Learn more about sun at;
https://brainly.com/question/15837114
#SPJ2
A concave mirror with a radius of curvature of 20 cm has a focal length of
A. 40 cm
B. 20 cm
C. 10 cm
D. answer depends on the index of refraction of the air around the mirror
Answer:
A. 40 cm
Explanation:
For a curved mirror, the focal length is twice the radius of curvature of the mirror. In formula:
[tex]f=2R[/tex]
where
f is the focal length
R is the radius of curvature
The concave mirror in this problem has a radius of curvature of
R = 20 cm
so, its focal length is
[tex]f=2R=2(20 cm)=40 cm[/tex]
For a positive charge moving in the direction of the electric field,its potential energy increases and its electric potential decreases.its potential energy decreases and its electric potential decreases.its potential energy decreases and its electric potential increases.its potential energy and its electric potential both remain constant.its potential energy increases and its electric potential increases.
Answer:
its potential energy decreases and its electric potential decreases.
Explanation:
Let's consider a radial field for simplicity. We have:
- The electric potential of the field is given by:
[tex]V=\frac{kQ}{r}[/tex]
where
k is the Coulomb's constant
Q is the charge source of the field
r is the distance from Q
We see that the electric potential decreases as we move away from the source. If we consider a positive charge q moving in the direction of the electric field, this charge q will move away from the charge Q (because the field lines generated by the positive particle Q point away from the particle), so the electric potential will decrease.
- The potential energy of the moving charge is given by
[tex]U=qV[/tex]
where q is the magnitude of the charge. As we said previously, V is decreasing while the charge is moving in the direction of the field, so since U is directly proportional to V, U will decrease as well.