100 POINTS!! 1. Calculate the current flowing when:

(A) 75 mC pass a point in I min;
(B) 0.5 GC pass a point in 2 hours;
(C) 2.0 MC pass a point in 1000 hours.

2. Calculate the charge flow when the current flow is:

(A) 6.0 A for 5 min;
(B) 250 mA for 4 hours;
(C) 2.5 KA for 50 s.

3. How long does it take for the following to pass a point in the circuit?

(A) 25 MC at a current of 25 mA;
(B) 48 C at a current of 12 A;
(C) 360 C at a current of 4.0 A.

4. A current of 10 cA flows through a resistor of resistance 4.0 ohms
Find the:
(a) P.d across the resistor;
(b) Total charge flow in 3 minutes;

To the left. When a force is applied to stop it from moving, frictional force provides resistance.It always moves in the opposite direction of an item in motion

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The magnitude of the acceleration of the boy and the girl is 5 m/s².

The magnitude of the acceleration of the boy and the girl is determined by applying Newton's second law of motion as shown below.

F = ma

where;

substitute the given parameters and solve for the common acceleration of the boy and the girl

a = T/(m₁+ m₂)

a = (300 N) / (35 kg + 25 kg)

a = 5 m/s²

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The kinetic energy of the car in kilojoules is 447 KJ.

The kinetic energy of the car is, E = 1/2 m[tex]v^{2}[/tex]

The velocity of the car is,  v = v (1000m/3600s)

V = 23.5 m/s

The kinetic energy of the car in joules is,

E = 1/2m[tex]v^{2}[/tex]

E = 1/2 (1621)(23.5)

E = 447KJ

An object's kinetic energy is the power it draws from movement. It is described as the amount of effort required to accelerate a body of a specific mass from rest to its specified velocity. The body keeps its kinetic energy after gaining it during acceleration, barring changes in speed. When slowing down from its current pace to a condition of rest, the body expends the same amount of energy. Any term in a system's Lagrangiam that has a derivative with respect to time is formally referred to as having kinetic energy.

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Using the concepts of atwood machine, we got 4.05m[tex]s^{-2}[/tex]. is the acceleration of system when released from rest.

We know very well that in atwood`s two bodies having different mass are hanged around the pulley.

The accceleration of the atwood is given by :

a=((m2-m1)/(m2+m1))×g, where m2 is the mass of heavier body,m1 is the mass of lighter body and g is the acceleration due to gravity.

So, according to question m2=11.9,m1=4.93 and g=9.8

So, on putting the value in above formula, we got

a=[(11.9-4.93)/(11.9+4.93)]×9.8

=>a=[(6.97)/(16.83)]×9.8

=>a=4.05m[tex]s^{-2}[/tex].

Hence, an  atwood machine in which two masses: one of mass 4.93 kg and the other of mass 11.9 kg. when released from rest, the acceleration of the system is 4.05m[tex]s^{-2}[/tex].

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In a collision between two unequal masses, the smaller mass by the larger mass compare with the impulse imparted to the larger mass by the smaller one they are equal.

Any incident where two or more bodies exert forces on each other quickly is referred to as a collision in physics. In physics, collision, which is also known as impact, is the abrupt, forceful coming together in close proximity of two bodies, such as, for instance, two pool balls, a golf club and a ball, a hammer and a nail head, two railroad cars when coupled, or a falling object and a floor. In physics, a collision occurs when particles, aggregates of particles, or solid bodies move in the same direction and get close enough to each other to interact and have an impact on one another. Distracted driving is the most frequent reason for an auto accident. Speeding, disobeying traffic signs, making improper turns, and driving while intoxicated or drugged-up are additional risk factors for car accidents.

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Answer:

C) 490

Explanation:

Normal force = mass × gravitational acceleration

50kg × 9.8

490 N

The initial velocity is -25m/s.

What is velocity?

Velocity, which is a vector quantity, is referred to as the "pace at which an item changes its position." Imagine someone moving quickly, constantly going back to their starting position after taking one step forward. The velocity would be zero, even though there might be a frenzy of activity as a result.

What is acceleration?

Acceleration is the rate at which the direction and speed of motion change over time. Anything is said to have been accelerated when it moves straighter and faster or slower. Motion on a circle accelerates even though the speed is constant because the direction is constantly changing.

Is up in physics positive or negative?

If you choose to make the upward direction negative and the downward direction positive (the commonly accepted convention), then g will be positive if the object is stationary or moving downwards. If an object is moving upward, g will be negative.

Therefore, the initial velocity is -25m/s.

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The wool becomes positively charged because it gives up electrons to the rubber rod whereas wool is rubbed against a Nylon strip so the wool will steal electrons from the Nylon and form a negative charge.

When the woolen cloth is stroke against the plastic, both wood and plastic get electrified due to friction built while rubbing. So, plastic has greater electron affinity (ability to attract electrons) in a contrast to wool, therefore, plastic acquires a negative charge and wool obtains a positive charge. When you rub a balloon with a cloth made of wool, the balloon captures electrons from the wool, leaving the balloon with a negative charge and the wool with a positive charge. If both balloons are pat with wool, they will both have the same charge (negative) and therefore will repel each other.

So we can conclude that Wool is a conductive material, which means it readily gives away its electrons. accordingly, when you rub a balloon on wool.

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the linear separation d at the retina is 5.73micrometers

diameter=2mm

lambda=500nm

nair=1.33

d=2.5cm

alpha=1.22lambda/nd

=1.22(500x10^9)/(1.33)(2x10^-3)

=2.3x10^-4 rad

D=(2.3x10^-4)(.025)=5.73micrometers

The area of the eye that transforms light into neural signals is called the retina (Latin: rete, "net"). Most vertebrates and some molluscs have this innermost, light-sensitive layer of tissue in their eyes. A two-dimensional representation of the visual world is created on the retina by the optics of the eye (cornea and lens); some of the image is in focus and some of the image is out of focus. Visual perception is produced by the retina's processing of the image and the optic nerve's transmission of nerve impulses to the visual cortex. Similar to a camera's image sensor, the retina fulfills a purpose.

The neural retina is supported by an outer layer and is made up of numerous layers of neurons coupled by synapses.

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The situation that would be most appropriate to the use a vector quantity is determining the net force that is acting on an object.

option A is the correct answer.

Vector quantities are the physical quantities characterized by the presence of both magnitude as well as direction.

Examples of vector quantities include the following;

Scalar quantities, are those physical quantities that have only magnitude without direction. Example is temperature.

Thus, the situation that would be most appropriate to the use a vector quantity is the situation that needs to be described by both magnitude and direction.

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The magnitude of the student's resultant displacement is 50 m.

To find the magnitude of displacement we must make all the paths.

Look at the picture

d² = 40²+30²

d² = 1,600+900

d² = 2,500

[tex]d \:=\: \sqrt{2,500}[/tex]

d = 50 m

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The width of the central maximum is 1.9×10-3 m.

For the distance L, where

light wavelength λ= 585 nm =585 x 10-9 m

Slit width yields sw =0.80 mm= 0.80 x 10-3 m

(a) First, we deduce that the minimum integer value m= 1 for the central maximum distance yields a minimum diffraction value from the center distance as Yc=0.95 mm 0.95 x 10-3 m. This relationship can be

calculation:-

yc=L sinθ=L(mλ/sw)  ----------(1)

Therefore, rearranging terms from the above equation, we get:

L=sw/λ(yc)

Whereby substituting initial values, the screen distance equation produces:

L=[(0.80×10-3)/(585×10-9)](0.95×10-3)

  =1.3 m

(b) Now, we deduce that the central maximum yields from equation (1):

W = 2 (yc)

Therefore, substituting initial values, we get:

W = 2 (0.95 x 10-3 m)

   =1.9×10-3 m

Wavelength is the distance among the same points (adjacent crests) within the adjoining cycles of a waveform signal propagated in space or along a wire. The wavelength is the distance between two wave crests, and it will likely be the same for troughs. The frequency is the number of vibrations that bypass a given spot in a single.

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The method of radiation is faster through a vacuum, the method of convection is faster through a gas and the method of conduction is faster through a solid.

There are three modes of heat transfer:

conduction

convection, and

radiation

Radiation:

The emission of energy as electromagnetic waves or as moving subatomic particles, especially high-energy particles causes ionization. As we know vacuum does not require any medium so radiation is the heat transfer which is faster in a vacuum.

Therefore we get that in vacuum radiation, solid conduction, and gas convection heat transfer is faster.

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Using the supposition that there is no friction and disregarding air resistance, the speed of the cart at the bottom of the hill is 24.6ms.

Small bumps collide with one another as surfaces move over one another. Friction acts as a resisting force on the surface's motion. Friction can be reduced by lubricants.

The friction caused by a moving item is inversely propotional and runs perpendicular to it. The type of surface the thing is in touch with determines the amount of friction it experiences. As long as there is a point of contact, friction remains independent of a area of contact.

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With an astronomical telescope, the angle of just resolution light from two stars would be greater if the light of the average star is red or if it is blue.

What is an astronomical telescope?

An astronomical telescope consists of two lenses: objective and eyepiece.

The objective lens forms the image of a far off object at focal point while eyepiece lens just magnifies the image and make it look more clear, visible and magnified.

The formula D = 1.22λ/dФ is used to find the value of aperture of the telescope.

In general, an astronomical telescope is used to view distant stars. Thus, the angle formed would be greater if the light emitted by the average stars is red or blue.

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The car travels a distance of 50ft before stopping, at a rate of 40 ft/sec when the brakes are applied. the car deceleration at a constant rate of 16 ft/sec^2.

Given , Initial speed of the coz ( Vo ) = 40 ft/ sec

Deceleration of the car (dv/dt ) = - 16 Ft/ sec^2

Final speed of the car (Vx ) = 0 Ft / sec

Let the distance travelled by the can be x at

any time t. Let u be the velocity at any time t .

Now , deceleration means rate of decrease of velocity.

So ,

dv/dt = - 16 ft / sec^2

decreasing with

Negative sign means the velocity is decreasing with time .

dv/dt = dv/dx(dx/dt)

dv/dx(dx/dt) = -16

dx/dt = v, so

v dv/dx = -16

vdv = -16 dx

Integrating both sides under the limit 40 to o

0 to x for 'x '. This gives

[tex]\int\limits^0_ a {v} \, dx = \int\limits^0_x {-16} \, dx[/tex]

Here, a=40

x=800/16

x=50ft.

The car travels a distance of 50ft

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To find the speed of electrons, known the accelerated and wavelength.

What is acceleration?

The rate of change in both speed and direction of velocity over time is defined as acceleration. When anything moves faster or slower in a straight line, it is said to have been accelerated. Because the direction is always shifting, motion on a circle accelerates even when the speed is constant.

What is wavelength?

A waveform signal's wavelength is defined as the separation between two identical points (adjacent crests) in adjacent cycles as the signal travels through space or along a wire. This length in wireless systems is typically expressed in meters (m), centimeters (cm), or millimeters (mm).

λ=h/p

⇒ 200pm=h/m×v

V=6.626×10^⁻³⁴/9.1×10^⁻³¹×200×10^⁻¹²

=0.00364×10^⁻³⁺¹²

=0.00364×10⁹

v⇒3.64×10⁶m/s

Therefore, the speed of the electron accelerated to 3.64×10⁶m/s attain this wavelength.

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Answer:  at least 180 degrees

The magnetic field is [tex]\vec{m}=\frac{Q}{3} R^2 \vec{\omega}[/tex]

The magnetic influence on moving electric charges, electric currents, and magnetic materials is described by a magnetic field, which is a vector field. A force perpendicular to the charge's own velocity and the magnetic field acts on it when the charge is moving through a magnetic field.

Uniformly charged spherical shell of radius R carries a total charge =Q

Hence it has surface charge density

[tex]\sigma=\frac{Q}{4 \pi R^2}[/tex]

It rotates about its axis with frequency=f

∴ Its angular velocity ω=2πf

Suppose the angular velocity [tex]\vec{\omega}=\omega \hat{z}[/tex]

To find the magnetic moment of spinning shell we can divide

it into infinitesimal charges. Using spherical polar coordinates (ρ,ϕ,θ) with origin at the center of the spherical  shell, we consider infinitesimal area dS of a circular ring of infinitesimal width and of radius r located at a distance R from the origin on the surface of sphere.

Here [tex]\vec{r}=R \sin \theta \hat{r}[/tex] and coordinate ρ=R, is constant for each elemental area.

[tex]d q=\sigma d S=\sigma R^2 \sin \theta d \theta d \phi[/tex]

Current in the ring is given by

[tex]\begin{aligned}&d I=(d q) \times f=\left(\sigma R^2 \sin \theta d \theta d \phi\right) \times \frac{\omega}{2 \pi} \\&\Rightarrow d I=\frac{\omega \sigma R^2 \sin \theta d \theta d \phi}{2 \pi}\end{aligned}[/tex]

Now the magnetic dipole moment of ring is given by the expression in terms of position vector [tex]\vec{r}[/tex]current density [tex]\vec{J}[/tex]

[tex]\begin{aligned}&d \vec{m}=\frac{1}{2} \int_{\text {ring }} \vec{r} \times \vec{J} \\&\Rightarrow d \vec{m}=\frac{1}{2} d I \int_{\text {ring }} \vec{r} \times d \vec{l}\end{aligned}[/tex]

Line integral becomes equal to the circumference of ring

[tex]\therefore d \vec{m}=d I\left(\pi R^2 \sin ^2 \theta\right) \hat{z}[/tex]

Inserting value of dI we get

[tex]\begin{aligned}&d \vec{m}=\frac{\omega \sigma R^2 \sin \theta d \theta d \phi}{2 \pi}\left(\pi R^2 \sin ^2 \theta\right) \hat{z} \\&\Rightarrow d \vec{m}=\frac{\vec{\omega} \sigma R^4 \sin ^3 \theta d \theta d \phi}{2}\end{aligned}[/tex]

Total magnetic moment is integral with respect to both variables within respective limits

[tex]\begin{aligned}&\vec{m}=\frac{\vec{\omega} \sigma R^4}{2} \int_0^\pi \sin ^3 \theta d \theta \int_0^{2 \pi} d \phi \\&\Rightarrow \vec{m}=\frac{\vec{\omega} \sigma R^4}{2} \times \frac{4}{3} \times 2 \pi \\&\Rightarrow \vec{m}=\frac{4}{3} \pi \sigma R^4 \vec{\omega}\end{aligned}[/tex]

Rewriting in terms of charge Q

[tex]\begin{aligned}&\vec{m}=\frac{4}{3} \pi\left(\frac{Q}{4 \pi R^2}\right) R^4 \vec{\omega} \\&\vec{m}=\frac{Q}{3} R^2 \vec{\omega}\end{aligned}[/tex]

The complete question is : A spherical shell of radius R and uniformly charged with charge Q is rotating about its axis with frequency f. Find the magnetic moment of the sphere?

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a) The frequency of fundamental mode of vibration of steel piano is 400Hz.

b) The number of the highest harmonic that could be heard by a person is 24ᵗʰ.

In the given question we have,

lenth of steel piano wire (L) = 0.4 m

tension/ force on steel piano (T) = 800N

mass of steel piano (m) = 3g = 0.003 kg

We shall find out the frequency of fundamental mode of vibration of steel piano.

Fundamental Frequency of object depends on wave speed in turn which depend on tension .

Using Fundamental Frequency,

f₁ = v/2L

where , v---> wave speed

f₁ ---> fundamental frequency

L ---> length of wire

Firstly, we have to find out the value of wave speed.

For determining the wave speed we use following relation,

v = sqrt ( T/ μ )

where, v---> wave speed

T ---> Tension or force

μ ----> mass per unit length = m/L

Now, put all given values in formula

μ = m/L = 0.003/0.4 kg/m =

v = √800×0.40/(3× 10⁻³) = 327m/sec

fundamental frequency (f₁) = 327/(2×0.4 )

= 400Hz

b) The nth harmonic has frequency , fₙ = n f₁

wher, f₁---> fundamental frequency

fₙ----> highest frequency

n ----> harmonic number

fₙ = 10,000 Hz , f₁ = 409Hz

put in above formula, 10,000 = n × 409

=> n = 100/4 = 24.4

So, 24th harmonic is the highest harmonic that could be heard by a person who is capable of hearing frequenies upto 10,000Hz.

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Electromagnetic radiation consists of particles called photons, which exhibit both wavelike and particle-like behavior. The greater the momentum of a photon, the longer its wavelength.

Electromagnetic radiation (or EM radiation) is energy that is transmitted through oscillating electric and magnetic fields at the speed of light. Electromagnetic radiation contains neither mass nor charge, but it travels in packets of radiant energy called photons. Electromagnetic waves carry energy and transfer it upon interaction with matter.

Electromagnetic radiation can take many forms, such as microwaves, infrared light, visible light, UV light, X-rays and the like.

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The gravitational force between the asteroids with masses 3. 71 x 10^5 kg and 1. 88 x 10^4 kg are separated by a distance of 1,300 m is 27.5 * 10^-8 N

F = G m1 m2 / r²

F = Gravitational force

m1 , m2 = Masses

r = Distance between m1 and m2

m1 = 3.71 * 10^5 kg

m2 = 1.88 * 10^4 kg

r = 1300 m

G = 6.67 * 10^-11 N m² / kg²

F = 6.67 * 10^-11 * 3.71 * 10^5 * 1.88 * 10^4 / 1300²

F = 46.52 * 10^-2 / 169 * 10^4

F = 27.5 * 10^-8 N

According to Newton's law of gravitation, any matter in the universe attracts another matter with a force. This force of attraction is directly proportional to the product of their masses and inversely proportional to the square of distance between them.

Therefore, the gravitational force between the asteroids is 27.5 * 10^-8 N

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The torque on the wheel is 0.0294 Nm

The term "torque" was coined by the ancient Romans. They described these necklaces with the Latin word "Torquere", a twisted helix, a spiral, which means "twist" and "turn".

Torque is a measure of the force that rotates an object around an axis. Torque causes an object to undergo angular acceleration in the same way that force accelerates an object in linear kinematics. Torque is a vector quantity. Newton meter is the unit of torque.

Torque = Force × Perpendicular distance line of action of force and axis

τ = mg × L

τ = 0.01 × 9.8 × 0.3

τ = 0.0294 Nm

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We can contrast distant galaxies with nearby galaxies.

Although scientists are unsure of the universe's actual age, we estimate that it is somewhere between 13 and 14 billion years old. In order to determine the age of the universe, astronomers use two different methods: (a) searching for the earliest stars; and (b) measuring the universe's rate of expansion and projecting it back to the Big Bang.

The amount of time it took for the galaxies to get to their current distances is therefore t=D/v. However, we know that v=H0D because to Hubble's Law. Therefore, t=D/v=D/(H0D)=1/H0. Thus, 1/H0 can be used as a rough estimate for the  age of the Universe.

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The final gravitational force at the surface of the star is 49 times of the initial gravitational force.

The attraction that exists between all masses in the universe, particularly between the mass of the earth and objects that are close to its surface.

Use Newton's gravitational law to find the gravitational force at the surface of a star if the star contracted to one fifth of its previous diameter as follows.

Newton's gravitational law states that the gravitational force between two objects is inversely proportional to the square of their distance and directly proportional to the product of their masses.

[tex]F_g}[/tex] =GMm/r²

In this case, the two objects' masses are M and m, G is the gravitational constant, and r is their separation from one another.

Since mass is constant, the gravitational force at the surface of a star before contraction is,

F₁ =GMm/r₁²

Here, r₁ is initial diameter of the star.

The gravitational force at the surface of a star after the contraction is,

F₂ =GMm/r₂²

Here, r₂ is final diameter of the star.

Compare the equations, we get

F₂/F₁= GMm/r₂²/GMm/r₁²

F₂/F₁=(r₁/r₂)²

F₂ = F₁(r₁/r₂)²

Substitute r₁/7 for r₂ in equation and solve for final gravitational force on the star.

F₂ = F₁(r₁/r₁/7)²

F₂= 49F₁

Therefore, the final gravitational force at the surface of the star is 49 times of the initial gravitational force.

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A block of mass 0.260 kg is placed on top of a light, vertical spring of force constant 5 025 n/m and pushed downward. After the block is released, the spring will travel upward to the maximum height of 10.86 meters.

The relation between the potential energy on a string and the length it stretches is given by:

E = 1/2 . kx²

Where:

k  = spring constant

x = spring stretch or compression

In the given problem:

k = 5,025 N/m

x = 0.106 m

Hence,

E = 1/2 . 5025 . (0.106)²

m . g . h =  1/2 . 5025 . (0.106)²

Where;

m = mass

h = height from the release point.

Hence,

0.260 x 10 x h = 28.23

h = 10.86 m

Therefore, the spring will travel upwards up to 10.86 m

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The constant force applied parallel to the plane required to cause a 15kg box to line up is 127.31 N.

Acceleration is the rate of change of the velocity of an item with appreciation to time. Accelerations are vector portions. The orientation of an item's acceleration is given by the orientation of the net pressure appearing on that object.

Calculation:-

mass =15 kg

Normal force = mgCos30°

parallel force = mgsin30°

acceleration required = 1.2 m/s²

Contact force = 15 × 9.8 × √3/2

                      = 127.31 N

Acceleration is the charge at which velocity modifications with time, in terms of each speed and route. A factor or an object moving in a straight line is accelerated if it quickens or slows down. Movement on a circle is extended despite the fact that the rate is consistent because the course is continually changing.

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When an imbalanced force is applied to a mass, an acceleration results. When the same unbalanced force is applied to a mass that is half as large, the resulting acceleration doubles.

The rate at which an object's velocity with respect to time changes is called its acceleration. The vector quantity of accelerations (in that they have magnitude and direction). The direction of the net force acting on an object determines its acceleration in relation to that force.

An influence that can alter an object's motion is known as a force. A force can cause an object with mass to change its velocity, or accelerate (for example, moving from a condition of rest). Intuitively, a push or a pull can also be used to describe force.

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.

According to the idea behind active galactic nuclei, heated plasma in an accretion disc that revolves around the black hole is principally responsible for the active galactic nucleus' high luminosity.

An active galactic nucleus (AGN) is a compact area at the Centre of a galaxy that exhibits features that indicate the luminosity is not coming from stars and is substantially brighter than usual over at least some of the electromagnetic spectrum. Is called active galactic nucleus.

A light-emitting object's radiant power, which is measured in absolute terms as luminosity, is the electromagnetic power that it radiates out over time. The total quantity of electromagnetic energy released by a star, galaxy, or other celestial object in a given amount of time is measured as luminosity in astronomy.

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The momentum of a single photon in the pulse is 1.19 * 10^-27 kg m/s.

It is the quantity of motion of a moving body, measured as a product of its mass and velocity.

How to calculate the momentum of a single photon in the pulse?
Wavelength of light is given,
λ = 556nm = 556 * 10^-9m

Wavelength and momentum (p) are related by
λ = h/p

Where h is the planck constant = 6.63 * 10^-34 m^2 kg/s

So, the momentum is

p = h/λ

[tex]\frac{6.63*10^{-34} }{ 556*10^{-9}}[/tex]

p = 1.19 * 10^-27 kg m/s

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