The heat emitted from anything is carried in the form of infrared waves. (C)
Refer the attached photo
Answer:
A
Explanation:
since the wooden bat is an opaque object placed after a translucent object, light will come through the plastic sheet but will be unable to go through the bat. hence the dark shadow of the bat on a lit sheet
A long straight metal rod has a radius of 2.0 mm and a surface charge of density 0.40 nC/m2. Determine the magnitude of the electric field 3.0 mm from the axis.
Answer:
Explanation:
Gauss Theorem
E2πrL=o2πRL/εo
then
E=oR/(rεo)
E=(0.4*10^-9*2*10^-3) / (3*10^-3*8.85*10^-12)
= 30.13 N/C
What is the work-energy theorem equation?
Answer:
W = Fd = KE =1/2mv²
Explanation:
not sure if that's what your looking for but i'm pretty sure this is it.
At a certain instant, coil A is in a 10-T external magnetic field and coil B is in a 1-T external magnetic field. Both coils have the same area and are oriented at right angles to the field. Which coil will have a greater emf induced in it
Answer:
Impossible to know without more information about the fields.
Explanation:
Changing the magnetic field induces the external magnetic field, but the information regarding magnetic field variation is not provided. We need to required more information for this
Therefore according to the above explanation the correct option is Impossible to know without more information about the fields.
Hence, the b option is correct
Which types of basketball injuries do you believe the warm-up could prevent? Explain
Answer:
pulling a muscle. putting too much strain on a muscle causing a tear.
Explanation:
Doing warm ups help your muscles adjust to the full extent of a basketball game. Warming up is like stretching, helps your muscles adjust before going full out on the court.
Answer:
Jogging and skipping can prevent any kind of leg injury because they strengthen the whole leg. Walking on heels might prevent an injury to an ankle. I know that basketball players often roll their ankles when they land on other players’ feet after jumping. I haven’t figured out what walking backward could prevent. That might just be an exercise to build skill and agility rather than prevent any kind of injury.
Explanation:
Word for word from edmentum
Two cylindrical resistors are made from the same material. The shorter one has length L, diameter D, and resistance R1. The longer one has length 8L, diameter 4D, and resistance R2. How do the resistances of these two resistors compare
Answer:
the resistance of the longer one is twice as big as the resistance of the shorter one.
Explanation:
Given that :
For the shorter cylindrical resistor
Length = L
Diameter = D
Resistance = R1
For the longer cylindrical resistor
Length = 8L
Diameter = 4D
Resistance = R2
So;
We all know that the resistance of a given material can be determined by using the formula :
[tex]R = \dfrac{\rho L }{A}[/tex]
where;
A = πr²
[tex]R = \dfrac{\rho L }{\pi r ^2}[/tex]
For the shorter cylindrical resistor ; we have:
[tex]R = \dfrac{\rho L }{\pi r ^2}[/tex]
since 2 r = D
[tex]R = \dfrac{\rho L }{\pi (\frac{2}{2 \ r}) ^2}[/tex]
[tex]R = \dfrac{ 4 \rho L }{\pi \ D ^2}[/tex]
For the longer cylindrical resistor ; we have:
[tex]R = \dfrac{\rho L }{\pi r ^2}[/tex]
since 2 r = D
[tex]R = \dfrac{ \rho (8 ) L }{\pi (\frac{2}{2 \ r}) ^2}[/tex]
[tex]R = \dfrac{32\rho L }{\pi \ (4 D) ^2}[/tex]
[tex]R = \dfrac{2\rho L }{\pi \ (D) ^2}[/tex]
Sp;we can equate the shorter cylindrical resistor to the longer cylindrical resistor as shown below :
[tex]\dfrac{R_s}{R_L} = \dfrac{ \dfrac{ 4 \rho L }{\pi \ D ^2}}{ \dfrac{2\rho L }{\pi \ (D) ^2}}[/tex]
[tex]\dfrac{R_s}{R_L} ={ \dfrac{ 4 \rho L }{\pi \ D ^2}}* { \dfrac {\pi \ (D) ^2} {2\rho L}}[/tex]
[tex]\dfrac{R_s}{R_L} =2[/tex]
[tex]{R_s}=2{R_L}[/tex]
Thus; the resistance of the longer one is twice as big as the resistance of the shorter one.
Transverse waves are sent along a 4.50 m long string with a speed of 85.00 m/s. The string is under a tension of 20.00 N. What is the mass of the string (in kg)?
Answer:
m = 0.0125 kg
Explanation:
Let us apply the formula for the speed of a wave on a string that is under tension:
[tex]v = \sqrt{\frac{F}{\mu} }[/tex]
where F = tension force
μ = mass per unit length
Mass per unit length is given as:
μ = m / l
where m = mass of the string
l = length of the string
This implies that:
[tex]v = \sqrt{\frac{F}{m/l} }\\ \\v = \sqrt{\frac{F * l}{m} }[/tex]
Let us make mass, m, the subject of the formula:
[tex]v^2 = \frac{F * l}{m}\\\\m = \frac{F * l}{v^2}[/tex]
From the question:
F = 20 N
l = 4.50 m
v = 85 m/s
Therefore:
[tex]m = \frac{20 * 4.5}{85^2}\\\\m = \frac{90}{7225}\\ \\m = 0.0125 kg[/tex]
(5 pt) You tie a cord to a pail of water, and your swing the pail in a vertical circular 0.700 m. What is the minimum speed must you give the pail at the highest point of the circle if no water is to spill from it
Answer:
The minimum speed required is 2.62m/s
Explanation:
The value of gravitational acceleration = g = 9.81 m/s^2
Radius of the vertical circle = R = 0.7 m
Given the mass of the pail of water = m
The speed at the highest point of the circle = V
The centripetal force will be needed must be more than the weight of the pail of water in order to not spill water.
Below is the calculation:
[tex]\frac{mV^{2}}{R} = mg[/tex]
[tex]V = \sqrt{gR}[/tex]
[tex]V = \sqrt{9.81 \times 0.7}[/tex]
[tex]V = 2.62 m/s[/tex]
A rod has length 0.900 mm and mass 0.500 kgkg and is pivoted at one end. The rod is not uniform; the center of mass of the rod is not at its center but is 0.500 mm from the pivot. The period of the rod's motion as a pendulum is 1.49 ss. What is the moment of inertia of the rod around the pivot
Answer:
The moment of inertia is [tex]I =0.14 \ kg \cdot m^2[/tex]
Explanation:
From the question we are told that
The length of the rod is [tex]l = 0.900 \ m[/tex]
The mass of the rod is [tex]m = 0.500 \ kg[/tex]
The distance of the center of mass from the pivot is [tex]d = 0.500 \ m[/tex]
The period of the rod's motion is [tex]T = 1.49 \ s[/tex]
Generally the period of the motion is mathematically represented as
[tex]T = 2 \pi * \sqrt{\frac{I}{m* g * d} }[/tex]
Where [tex]I[/tex] is the moment of inertia about the pivot so making [tex]I[/tex] the subject of formula
[tex]I = [\frac{T}{2\pi } ]^2 * m * g * d[/tex]
substituting values
[tex]I = [\frac{1.49}{2* 3.142 } ]^2 * 0.5 * 9.8 * 0.5[/tex]
[tex]I =0.14 \ kg \cdot m^2[/tex]
How much heat had to be put in during the process to increase the internal energy of the gas by 2.00×104 JJ ?
Complete question:
The pv diagram in the figure below (see attached file) shows a process abc involving 0.920 of an ideal gas.
How much heat had to be put in during the process to increase the internal energy of the gas by 2.00×10⁴ J ?
Answer:
The amount of heat required to increase the internal energy of the gas is 2,000 J
Explanation:
Work done in gas is given as;
W = ΔPV
The pressure of the gas at "a" = 2 x 10⁵ Pa
The pressure of the gas at "b" = 5 x 10⁵ Pa
The volume of the gas at "a" = 0.01 m³
The volume of the gas at "b" = 0.07 m³
The work done = (5 x 10⁵ Pa - 2 x 10⁵ Pa) x (0.07 m³ - 0.01 m³)
The work done = 3 x 10⁵ Pa x 0.06 m³
The work done = 18000 J
The work done = 1.8 x 10⁴ J
Determine, the amount of heat required to increase the internal energy of the gas by 2.00×10⁴ J.
1.8 x 10⁴ J + H = 2.00 x 10⁴ J
H = 2.00 x 10⁴ J - 1.8 x 10⁴ J
H = 0.2 x 10⁴ J
H = 2,000 J
Therefore, the amount of heat required to increase the internal energy of the gas by 2.00×10⁴J is 2,000 J
A particle accelerator fires a proton into a region with a magnetic field that points in the +x-direction (a) If the proton is moving in the ty-direction, what is the direction of the magnetic force on the proton? +x-direction -x-direction +y-direction -y-direction +z-direction -z-direction zero force What is the formula used to find the vector magnetic force? What is the right-hand rule for a cross prod (b) If the proton is moving in the -y-direction, what is the direction of the magnetic force on the proton? +x-direction -x-direction +y-direction -y-direction +z-direction -z-direction zero force (c) If the proton is moving in the x-direction, what is the direction of the magnetic force on the proton?
Answer:
a) -z direction, b) +z direction, c) F=0
Explanation:
The magnetic force is given by the expression
F = q v x B
the bold indicate vectors, this equation can be separated in its module
F = a v B sin θ
and where θ is the angles between the speed and the magnetic field.
The direction of the force can be found with the right-hand rule. For a positive charge, the thumb goes in the direction of speed, the fingers extended in the direction of the magnetic field and the palm points in the direction of the force, if the charge is negative the force is in the opposite direction.
a) Let's apply this to our case
the proton is positively charged
moves in the direction of + x
The magnetized field goes in the direction of y
therefore applying the right hand rule the force must be in the direction of the negative part of the z-axis (-z)
The right-hand rule is used to find this address.
b) in this case it indicates that the proton moves in the recode of -y
again we apply the right hand rule and the force is in the direction of + z
c) The proton moves in the x direction
In this case the force is zero because the angle between the field and the speed is zero and the sine is zero, therefore the force is zero
A particle located at the position vector m has a force N acting on it. The torque about the origin is
Complete question:
A particle located at the position vector r = (i + j) m has a force F = (2i + 3j) N acting on it. The torque about the origin is
Answer:
The torque about the origin is (5k) N.m
Explanation:
The torque about the origin is the vector or cross product of the two vectors.
τ = r x F (N.m)
Where;
τ is the torque about the origin
τ = r x F
τ = (i + j) x (2i + 3j)
For cross product;
i x j = k
i x k = j
j x k = i
i x i = 0
j x j = 0
k x k = 0
τ = (i + j) x (2i + 3j)
τ = (i x 2i) + (i x 3j) + (j x 2i) + (j x 3j)
τ = (0) + (3k)+ (2k) + 0
τ = (5k) N.m
Therefore, the torque about the origin is (5k) N.m
In a high school swim competition, a student takes 1.6 s to complete 1.5 somersaults. Determine the average angular speed of the diver, in rad/s, during this time interval.
Answer:
The angular speed is [tex]w = 5.89 \ rad/s[/tex]
Explanation:
From the question we are told that
The time taken is [tex]t = 1.6 s[/tex]
The number of somersaults is n = 1.5
The total angular displacement during the somersault is mathematically represented as
[tex]\theta = n * 2 * \pi[/tex]
substituting values
[tex]\theta = 1.5 * 2 * 3.142[/tex]
[tex]\theta = 9.426 \ rad[/tex]
The angular speed is mathematically represented as
[tex]w = \frac{\theta }{t}[/tex]
substituting values
[tex]w = \frac{9.426}{1.6}[/tex]
[tex]w = 5.89 \ rad/s[/tex]
Molecules in the combustion chamber of a rocket engine are in a high state of random motion. When the molecules are expelled through a nozzle in a more ordered state, will their temperature be higher than, lower than, or the same as their initial temperature in the chamber before being exhausted?
Answer:
The temperature of molecules exhausted through the nozzle
is lower than the temperature in the chamber before being exhausted.
Explanation:
Final naïve case: If the highest-pitch string on the piano is made of spring steel (density = 7800 kg/m3) with a diameter of 1/32" (= 0.794 mm), what will the linear density of such a string be (in kg/m)?
Answer:
The linear density is [tex]K = 3.863 *10^{-3 } \ kg/m[/tex]
Explanation:
From the question we are told that
The density of steel is [tex]\rho = 7800 \ kg/m^3[/tex]
The diameter of the string is [tex]d = 0.794 \ mm = 7.94 *10^{-4} \ m[/tex]
The radius of the string is evaluated as [tex]r = \frac{D}{2} = \frac{7.94 *10^{-4}}{2} = 3.97*10^{-4} \ m[/tex]
The volume of the string is mathematically evaluated as
[tex]V = \pi * r ^2 * L[/tex]
Now assuming that the length of the string is L = 2 m
So
[tex]V = 3.142 * (3.97 *10^{-4})^2 * (2)[/tex]
[tex]V = 9.9041 *10^{-7} \ m^3[/tex]
Then the mass of the string would be
[tex]m = \rho * V[/tex]
substituting value
[tex]m = 7800*9.904 14 *10^{-7}[/tex]
[tex]m = 7.73*10^{-3} \ kg[/tex]
Looking at the question we see that the unit of the linear density is [tex]\frac{kg}{m}[/tex]
Hence the linear density is evaluated as
[tex]K = \frac{m}{L}[/tex]
substituting value
[tex]K = \frac{7.73 *10^{-3}}{2}[/tex]
[tex]K = 3.863 *10^{-3 } \ kg/m[/tex]
At what speed would a 3.00 x 10^4 kg airplane have to fly and with a momentum of 1.60 x 10^9 kg.m/s
Answer:
5.3×10⁴ m/s
Explanation:
From the question,
Momentum = mass× velocity
M = mV................ Equation 1
Where M = momentum of the airplane, m = mass of the airplane, V = Velocity of the airplane
make V the subject of the equation
V = M/m.................. Equation 2
Given: M = 1.6×10⁹ Kg.m/s, m = 3.0×10⁴ kg
Substitute these values into equation 2
V = 1.6×10⁹/3.0×10⁴
V = 5.3×10⁴ m/s
How many excess electrons must be distributed uniformly within the volume of an isolated plastic sphere 20.0 cm in diameter to produce an electric field of 1450 N/C just outside the surface of the sphere
Answer:
1.007 × 10^(10) electron
Explanation:
We are given;
Electric Field;E = 1450 N/C
Diameter;d = 20 cm = 0.2 m
So, Radius: r = 0.2/2 = 0.1 m
Formula for Electric field just outside the sphere is given by the formula;
E = kq/r²
Where;
E is the magnitude of the electric field. q is the magnitude of the point charge r is distance from the point charge
k is a constant with a value of 9 x 10^(9) N.m²/C²
Making q the subject, we have;
q = Er²/k
Thus,
q = 1450 × 0.1²/(9 × 10^(9))
q = 1.61 × 10^(-9) C
Now, total charge q is also given by the formula;
q = Ne
Where;
e is charge on electron which is 1.6 × 10^(-19)
N is number of excess electrons
Making N the formula, we have;
N = q/e
N = (1.61 × 10^(-9))/(1.6 × 10^(-19))
N = 1.007 × 10^(10) electron
Which of the following is not considered a behavior?
A. eating
B. anxiety
C. sleeping
D. crying
━━━━━━━☆☆━━━━━━━
▹ Answer
B. Anxiety
▹ Step-by-Step Explanation
Anxiety isn't a behavior since it's a feeling. Behavior and feeling are different things therefore, anxiety is the correct answer.
Hope this helps!
- CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
Eating, sleeping, and crying all are considered as behaviors. However, anxiety cannot be considered as a behavior because it is a feeling. Thus, the correct option is B.
What is Anxiety?Anxiety is an intense feeling of excessive, and persistent worry and the fear about everyday situations. This includes fast heart rate, rapid breathing, sweating, and feeling tired constantly may occur.
Behavior is the range of actions and mannerisms which are made by individuals, organisms, systems or the artificial entities in some environment. These systems can include other systems or organisms as well as the inanimate physical environment. Behaviors include eating, sleeping, and crying. Anxiety is not a behavior, it is a feeling.
Therefore, the correct option is B.
Learn more about Anxiety here:
https://brainly.com/question/28481974
#SPJ5
In the photoelectric effect, if the intensity of light shone on a metal increases, what will happen?
Answer:
C) There will be more electrons ejected
Explanation:
The number of electrons ejected whenever a photoelectric effect is identified it is proportional to the intensity of the incident light
Nevertheless, the photoelectrons' maximal kinetic energy is independent of their light intensity
Therefore, the maximum speed of the electron ejected doesn't really depend on the light intensity
So, if the intensity rises, only the number of electrons ejected will rised
Therefore the option c is correct
Answer:
C) There will be more electrons ejected
Explanation:
In the photoelectric effect, photons with an energy of E are shone upon a piece of metal, and if the energy of the photons overcome the work function ϕ of the metal, then electrons with will be ejected from the metal with a kinetic energy KE.
E_photon = Φ + KE
Each photon is capable of ejecting one electron from the metal. Therefore, increasing the intensity of the light (the number of photons shone on the metal) will increase the number of electrons ejected from the metal.
Four identical charges particles of charge 1Uc, 2Uc,
3Uc and 4Uc
are placed at x = lm, x=2m,
x=3m and
x=5m. The electric field intensity
at origin is?
Answer:
17.94 kN/C is the electric field intensity at the origin due to the charges.
Explanation:
From the question, we are told that
The distance of 1 μC from origin = 1 m
The distance of 2 μC from origin = 2 m
The distance of 3 μC from origin = 3 m
The distance of 4 μC from origin = 5 m
Therefore, for us to find the electric field intensity, we'll solve below:
The formula for Electric field intensity = ( k * q ) / ( r * r )
where , r is distance ,
k = 9 * 10^9 ,
and , q is charge .
now ,
electric field intensity at the origin = [ k * 10^(-6) / 1 * 1 ] +[ k * 2 * 10^(-6) / 2 * 2 ] + [ k * 3 * 10^(-6) / 3 * 3 ] + [ k * 4 * 10^(-6) / 5 * 5 ]
=> electric field intensity at the origin = k * 10^(-6) [ 1 + 1/2 + 1/3 + 4/25 ] N/C
=> electric field intensity at the origin = 9 * 10^9 * 10^(-6) * 1.99 N/C
=> electric field intensity at the origin = 17.94 kN/C
A woman is standing at the rim of a nonuniform cylindrical horizontal platform initially at rest. The platform is free to rotate about frictionless orthogonal axle that goes through its center and has 4 m in diameter and moment of inertia of 500 kgm2. The woman then starts walking along the rim in clockwise direction at a constant speed of 1.50 m/s relative to the Earth. If a woman has 60 kg, how much work does she do to set herself and the platform into motion?
Answer:
e
Explanation:
i took it myself and got it right
Identify the term used to describe the ability of a liquid to flow against gravity up a narrow tube.
Answer:
This would be capillary action.
Explanation:
The physics behind it is gravity adhesion. The forces that attract between dissimilar molecules or atoms, in our case the contact area between the particles of the liquid and the particles forming the tube.
What is the purpose of guarding electrical equipment with exposed parts operating at 50 volts or more?
Answer:
Electrical equipment should be guarded with exposed parts operating at 50 volts or more to avoid the accidental shock and also to prevent accidental contact by workers and their tools.
Explanation:
Electrical guarding involves the process by which electrical equipment are enclosed so that people do not accidentally come in contact with it in order to avoid accidental shock.
Electrical components operating at 50 volts or more must be guarded with covers or other permanent barriers and it should be put where the people that are authorized to it have acess to it.
Which of the following controls the normal breathing system
A piece of purple plastic is charged with 9.31×106 extra electrons compared to its neutral state. What is its net electric charge (including its sign) in coulombs?
Answer:
Q = - 1.5 x 10⁻¹² Coulomb
Explanation:
While in the neutral state, the charge on the piece of purple plastic must be zero. So the net charge is due to the charge of the extra electrons. Therefore,
Q = ne
where,
Q = net charge on piece of purple plastic = ?
n = No. of extra electrons on piece of purple plastic = 9.31 x 10⁶ electrons
e = Charge on one electron = - 1.6 x 10⁻¹⁹ Coulomb
Therefore,
Q = (9.31 x 10⁶)(- 1.6 x 10⁻¹⁹ Coulomb)
Q = - 1.5 x 10⁻¹² Coulomb
A train at rest emits a sound at a frequency of 1057 Hz. An observer in a car travels away from the sound source at a speed of 20.6 m/s. What is the frequency heard by the observer
Answer:
993.52 Hz
Explanation:
The frequency of sound emitted by the stationery train is 1057 Hz.
The car travels away from the train at 20.6 m/s.
The frequency the observer hears is given by the formula:
[tex]f_o = \frac{v - v_o}{v}f[/tex]
where v = velocity of sound = 343 m/s
vo = velocity of observer
f = frequency from source
This phenomenon is known as Doppler's effect.
Therefore:
[tex]f_o = \frac{343 - 20.6}{343} * 1057\\ \\f_o = 322.4 / 343 * 1057\\\\f_o = 993.52 Hz[/tex]
The frequency heard by the observer is 993.52 Hz.
An alpha particle (charge +2e) and an electron move in opposite directions from the same point, each with the speed of 2.80×10^5 m/s . Find the total magnetic field these charges produce at point P, which is 8.25 nm from each charge. μ0=4πx10^-7 H/m, 1nm= 10^-9 m.
Answer:
Explanation:
Magnetic field due to moving charge =
[tex]B=\frac{\mu_0}{4\pi} \times \frac{qv}{r^2}[/tex]
q is charge moving with velocity v and r is distance from point at which field is calculated .
For alpha particle
[tex]B_1=\frac{\mu_0}{4\pi} \times \frac{2\times 1.6\times10^{-19}\times 2.8\times 10^5}{(8.25\times 10^{-9})^2}[/tex]
= 0.1316 x 10⁻³ T
For electron
[tex]B_2=\frac{\mu_0}{4\pi} \times \frac{ 1.6\times10^{-19}\times 2.8\times 10^5}{(8.25\times 10^{-9})^2}[/tex]
= .0658 x 10⁻³ T .
Both these magnetic field will be same in direction because direction of equivalent current is same for both the particles .
Hence
Total magnetic field
= B₁ + B₂ = .1974 x 10⁻³
= 1.974 x 10⁻⁴ T .
The total magnetic field produced by these charges at the given point is 1.98 x 10⁻⁴ T.
The given parameters;
charge of the alpha-particle, q = 2espeed of the charges, v = 2.8 x 10⁵ m/sseparation distance, r = 8.25 nmThe magnetic field produced by each charge is calculated using Biot-Savart law;
[tex]B = \frac{\mu _o q}{4\pi } \times \frac{v}{r^2} \\\\B_1 = \frac{(4\pi \times 10^{-7} ) \times (1.602 \times 10^{-19})}{4\pi } \times \frac{2.8 \times 10^5}{(8.25 \times 10^{-9} )^2}\\\\B_1 = 6.6 \times 10^{-5} \ T[/tex]
[tex]B_2 = \frac{(4\pi \times 10^{-7} ) \times (2\times 1.602 \times 10^{-19})}{4\pi } \times \frac{2.8 \times 10^5}{(8.25 \times 10^{-9} )^2}\\\\B_2 = 1.32 \times 10^{-4} \ T[/tex]
The total magnetic field produced by these charges at the given point P;
[tex]B_T = B_1 + B_2\\\\B_T = 6.6\times 10^{-5} \ + \ 1.32 \times 10^{-4}\\\\B_T = 1.98 \times 10^{-4} \ T[/tex]
Learn more here:https://brainly.com/question/12984403
An 100 V/m electric field is directed along the x axis. If the potential at the origin is 300 V, what is potential at the point ( -2m, 0) point
Answer:
200volts
Explanation:
Pls see attached file
Answer:
100 V
Explanation:
Electric field E = 100 V/m
Potential at the origin = 300 V
Potential at point (-2m, 0) i.e 2 m behind the origin = ?
From the equation ΔV = EΔd,
ΔV = [tex]V_{0} - V_{x}[/tex]
where [tex]V_{0}[/tex] is the potential at origin,
and [tex]V_{x}[/tex] is the potential at point (-2, 0)
E = electric field
Δd = 0 - (-2) = 2 m
[tex]V_{0} - V_{x}[/tex] = 300 - [tex]x[/tex]
equating, we have
300 - [tex]x[/tex] = 100 x 2
300 - [tex]x[/tex] = 200
[tex]x[/tex] = 100 V
Find the ratio of the gravitational force between two planets if the masses of both planets are quadrupled but the distance between them stays the same.
Answer:
The ratio of the new force over the original force is 16
Explanation:
Recall the formula for the gravitational force between two masses M1 and M2 separated a distance D:
[tex]F_G=G\,\frac{M_1\,\,M_2}{D^2}[/tex]
So now, if the masses M1 and M2 are quadrupled and the distance stays the same, the new force becomes:
[tex]F'_G=G\,\frac{4M_1\,\,4M_2}{D^2}=G\,\frac{16\,\,M_1\,\,M_2}{D^2}=16\,\,G\,\frac{M_1\,\,M_2}{D^2}= 16\,\,F_G[/tex]
which is 16 times the original force.
So the ratio of the new force over the original force is 16
The ratio of the gravitational force between two planets if the masses of both planets are quadrupled but the distance between them stays the same is 16:1.
What does Newton's law of gravitation state?Newton's law of gravitation states that any particle of matter in the universe attracts any other with a force varying directly as the product of the masses and inversely as the square of the distance between them.
The formula for Newton's law of gravitation is:
[tex]F = G \frac{m_1m_2}{r^{2} }[/tex]
where,
F is the gravitational force.G is the gravitational constant.m₁ and m₂ are the masses of both objects.r is the distance between the objects.The initial force between the planets is:
[tex]F_1 = G \frac{m_1m_2}{r^{2} }[/tex]
The force between the planets if the masses of both planets are quadrupled but the distance between them stays the same is:
[tex]F_2 = G \frac{4m_14m_2}{r^{2} } = 16 G \frac{m_1m_2}{r^{2} }[/tex]
The ratio of F₂ to F₁ is:
[tex]\frac{F_2}{F_1} =\frac{16 G \frac{m_1m_2}{r^{2} }}{G \frac{m_1m_2}{r^{2} }} = \frac{16}{1}[/tex]
The ratio of the gravitational force between two planets if the masses of both planets are quadrupled but the distance between them stays the same is 16:1.
Learn more about Newton's gravitational law here: https://brainly.com/question/9373839
Two long, parallel wires carry currents in the same direction. If I1 = 10 A, and I2 = 20 A, and they are d = 1.0 m apart, what is the magnetic field at a point P midway between them?
Answer:
The magnetic field at mid point between two parallel wires is 1.2 x 10⁻⁵ T
Explanation:
Given;
current in the first wire, I₁ = 10 A
current in the second wire, I₂ = 20 A
distance between the two wires, d = 1.0 m
Magnetic field at mid point between two parallel wires is calculated as;
[tex]B = \frac{\mu_o I_1}{2\pi r} + \frac{\mu_o I_2}{2\pi r} \\\\B = \frac{\mu_o }{2\pi r}(I_1 +I_2)[/tex]
where;
r is the midpoint between the wires, = 0.5 m
μ₀ is the permeability of free space, = 4π x 10⁻⁷
[tex]B = \frac{\mu_o }{2\pi r}(I_1 +I_2)\\\\B = \frac{4\pi*10^{-7} }{2\pi *0.5}(10 +20)\\\\B = \frac{4\pi*10^{-7} *30}{2\pi *0.5}\\\\B = 1.2 *10^{-5} \ T[/tex]
Therefore, the magnetic field at mid point between two parallel wires is 1.2 x 10⁻⁵ T