Monochromatic light of wavelength, λ is traveling in air. The light then strikes a thin film having an index of refraction n1 that is coating a material having an index of refraction n2. If n1 is larger than n2, what minimum film thickness will result in minimum reflection of this light?

Answer:

-50N

Explanation:

F=ma=m(Vf-Vi)/t

F=(10)(-10)/(2)=-50N

So the force acting on the block is -50N, where the negative sign simply tells us that the force is opposite to the direction of movement.

Answer:

a neutron star

Explanation:

Answer:

d

Explanation:

Answer:

 V = - 3.85 V

Explanation:

The electric potential of a continuous charge distribution is

       V = k ∫ dq / r

to find charge differential let's use the concept of linear density

        λ = dq / dx

       dq = λ dx

the distance from a load element to the point of interest

       x₀ = 23 cm = 0.23 m

       r = √ (x-x₀)² = x - x₀

we substitute

        v = k ∫ λ dx / (x-x₀)

we integrate and evaluate between x = 0 and x = l = 0.10 cm

       V = k λ [ln (x-x₀) - ln (-x₀)]

        V = k λ ln ((x-x₀) / x₀)

let's calculate

         V = 9 10⁹  0.74 10⁻⁹ ln ((0.23 - 0.10) / 0.23)

          V = - 3.85 V

Answer:

2960 N

Explanation:

Convert rev/min to rad/s:

150 rev/min × (2π rad/rev) × (1 min / 60 s) = 50π rad/s

Sum of forces in the centripetal direction:

∑F = ma

T = m v² / r

T = m ω² r

T = (0.2 kg) (50π rad/s)² (0.6 m)

T = 2960 N

Answer:

metal conducts heat better than wood.

Explanation:

Metals are generally good conductors of heat, and they usually conduct heat at a relatively rapid rate. Inside the room with a uniform temperature, a metal when touched will rapidly conduct the heat from your hand, leaving your hand with a cooler feeling. Wood on the other hand is a poor heat conductor, so the heat is not conducted from your hand fast enough to cool it up to the point that your hand feels cool.

Answer:

a) Your player

b) Observer's player

c) Each measures their own first

Explanation:

Because given problem is having relative velocity to each other. The person sitting on the train is moving with a very high speed relative to the person standing next to the track.

In this case, the clock situated in the train will be running slow with respect to the stationary frame of reference

Answer:

4.635 *10^12 Neutrinos

Explanation:

Here in this question, we are to determine the number of neutrinos in billions produced, given the power generated by the proton-proton cycle.

We proceed as follows;

In proton-proton cycle generates 26.7 MeV of energy and in this cycle two neutrinos are produced.

From the question, we are given that

Power P = 9.9 watts = 9.9 J/s

Watts is same as J/s

The number of proton-proton cycles required to generate E energy is N = E / E '

Where E ' = Energy generated in proton-proton cycle which is given as 26.7 Mev in the question

Converting Mev to J, we have

= 26.7 x1.6 x10 -13 J

To get the number N which is the number of proton-proton cycle required, we have;

N = 9.9 /(26.7 x1.6 x10^-13) = 2.32 * 10^12

Since we have two proton cycles( proton-proton), it automatically means 2 neutrinos will be produced.

Therefore number of neutrions produced = 2 x Number of proton-proton cycles = 2 * 2.32 * 10^12 = 4.635 * 10^12 neutrinos

Answer:

Both Ellen and Mary are correct.

Explanation:

Both are correct, it's just different ways of saying the same thing.

When the acceleration is always opposite in direction to the displacement, then, the acceleration is directly proportional to the displacement of an object from its equilibrium position

Answer:

(B) a whole number of wavelengths.

Explanation:

Two beams of coherent light start out at the same point in phase and travel different paths to arrive at point P. If the maximum destructive interference is to occur at point P, the two beams must travel paths that differ by a whole number of wavelengths.

When the resultant effect of the combination of two identical waves result in their annihilation or complete cancellation of the effect of each other, destructive interference takes place. Hence to have two wave sources producing waves that have the same frequency wavelength and amplitude and which are always in phase with each other or have a constant phase difference are said to be Coherent source

Answer:In the case of two proton beams the protons repel one another because they have the same sign of electrical charge. There is also an attractive magnetic force between the protons, but in the proton frame of reference this force must be zero! Clearly then the attractive magnetic force that reduces the net force between protons in the two beams as seen in our frame of reference is relativistic. In particular the apparent magnetic forces or fields are relativistic modifications of the electrical forces or fields. As such modifications, they cannot be stronger than the electrical forces and fields that produce them. This follows from the fact that switching frames of reference can reduce forces, but it can’t turn what is attractive in one frame into a repulsive force in another frame.

In the case of wires the net charges in two wires are zero everywhere along the wires. That makes the net electrical forces between the wires very nearly zero. Yet the relativistic magnetic forces and fields will be of the same sort as in the case of two beams of charges of a single sign. This is true even in the frame of reference of what we think as the moving charges, that is, the electrons. In the frame of reference moving at the drift velocity of these current-carrying electrons, it is the protons or positively charged ions that are moving in the other direction. Consequently in any frame of reference for current-carrying wires in parallel, the net electrical force will be essentially zero, and there will be a net attractive magnetic force

Explanation:                                                                              

Explanation:

Particles with similar charges (both positive or both negative) will always repel each other, regardless of their speed or direction.

Answer:

A. magnetic field

Explanation:

The magnetic field is produced around a wire when an electrical current is in the wire because of the magnetic effect of the electric current therefore the correct answer is option A .

A magnetic field could be understood as an area around a magnet, magnetic material, or an electric charge in which magnetic force is exerted.

As given in the problem statement we have to find out what is produced around a wire when an electrical current is in the wire.

The magnetic field is produced as a result when an electrical current is passed through the conducting wire .

Option A is the appropriate response because a wire's magnetic field is created when an electrical current flows through it due to the magnetic influence of the electric current .

Learn more about the magnetic fields here, refer to the link given below;

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Answer:infrared radiation

Explanation:

Infrared radiation and  microwave radiation  of the electromagnetic spectrum have longer wavelengths than visible light.

EM waves are another name for electromagnetic waves. When an electric field interacts with a magnetic field, electromagnetic waves are created. These electromagnetic waves make up electromagnetic radiations. It is also possible to say that electromagnetic waves are made up of magnetic and electric fields that are oscillating. The basic equations of electrodynamics, Maxwell's equations, have an answer in electromagnetic waves.

If we arrange   electromagnetic wave with decrease in wavelength, we get:

Radio waves > microwave >  Infrared >  Visible light > Ultraviolet > X-rays > Gamma radiation.

Hence,  Infrared  radiation and  microwave radiation  of the electromagnetic spectrum have longer wavelengths than visible light.

Learn more about electromagnetic wave here:

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Answer:

[tex]L = 109.01 db[/tex]

Explanation:

Given

Power, P = 100 W

Distance, d = 10 m

Required

Determine the Sound Level

First, the sound intensity as to be calculated; This is done, as follows;

[tex]I = \frac{P}{4\pi d^2}[/tex]

Substitute for P, d and take π as 3.14

[tex]I = \frac{100}{4 * 3.14 * 10^2}[/tex]

[tex]I = \frac{100}{4 * 3.14 * 100}[/tex]

[tex]I = \frac{100}{1256}[/tex]

[tex]I = 0.0796Wm^{-2}[/tex] --- Approximated

Next is to calculate the Sound Level, as follows

[tex]L = 10 * Log(\frac{I}{I_o})[/tex]

Where [tex]I_o = 10^{-12} Wm^{-2}[/tex]

Substitute for I and Io

[tex]L = 10 * Log(\frac{0.0796}{10^{-12}})[/tex]

[tex]L = 10 * Log(0.0796*10^{12)[/tex]

[tex]L = 10 * Log(0.0796*10^{12)[/tex]

[tex]L = 10 * 10.901[/tex]

[tex]L = 109.01 db[/tex]

Hence, the sound level is 109.01 decibels

Answer:

A. 4.82 cm

B. 24.66 cm

Explanation:

The depth of water = 19.6 cm

Distance of fish  = 6.40 cm

Index of refraction of water = 1.33

(A). Now use the below formula to compute the apparent depth.

[tex]d_{app} = \frac{n_{air}}{n_{water}} \times d_{real} \\= \frac{1}{1.33} \times 6.40 \\= 4.82 cm.[/tex]

(B). the depth of the fish in the mirror.

[tex]d_{real} = 19.6 cm + (19.6 cm – 6.40 cm) = 32.8 cm[/tex]

Now find the depth of reflection of the fish in the bottom of the tank.

[tex]d_{app} = \frac{n_{air}}{n_{water}} \times d_{real} \\d_{app} = \frac{1}{1.33} \times 32.8 = 24.66\\[/tex]

Answer:

True or False

Explanation:

Because.....

easy 50% chance you are right

Answer:

41.5 cm to the left of the observer

Explanation:

See attached file

Answer:

8 seconds

160 meters

Explanation:

Given in the y direction:

Δy = 0 m

v₀ = 40 m/s

a = -10 m/s²

Find: t

Δy = v₀ t + ½ at²

0 m = (40 m/s) t + ½ (-10 m/s²) t²

0 = 40t − 5t²

0 = 5t (8 − t)

t = 0 or 8

Given in the x direction:

v₀ = 20 m/s

a = 0 m/s²

t = 8 s

Find: Δx

Δx = v₀ t + ½ at²

Δx = (20 m/s) (8 s) + ½ (0 m/s²) (8 s)²

Δx = 160 m

Answer:

V = (k*Q)/R

Explanation:

Total potential difference accelerates the electron to being very far away from Q is;

V = (k*Q)/R

Where,

V is the Potential Difference in Joules per Coulomb

k is the constant

Q is the charge in Coulomb

R is Electron distance in cm or m

Example

An electron starts from rest 66.1 cm from a fixed point charge with Q = -0.120 μC. What total potential difference accelerates the electron from being very far away from Q

For k = 9.0*10^9 N*m^2/C^2

V = (k*Q)/R

V = (9.0*10^9 * -0.120*10^-6)/0.661

V = -1633.9 Volt.

The answer will change to positive because V = (k*Q)/R is negative at the outset and Zero far away.

The electron (with a negative charge) has a positive energy in the beginning and that gets converted into a positive kinetic energy "far away".

Answer:

[tex] \boxed{\sf Kinetic \ energy \ (KE) = 85 \ J} [/tex]

Given:

Mass (m) = 6.8 kg

Speed (v) = 5.0 m/s

To Find:

Kinetic energy (KE)

Explanation:

Formula:

[tex] \boxed{ \bold{\sf KE = \frac{1}{2} m {v}^{2} }}[/tex]

Substituting values of m & v in the equation:

[tex] \sf \implies KE = \frac{1}{2} \times 6.8 \times {5}^{2} [/tex]

[tex] \sf \implies KE = \frac{1}{ \cancel{2}} \times \cancel{2} \times 3.4 \times 25 [/tex]

[tex] \sf \implies KE =3.4 \times 25 [/tex]

[tex] \sf \implies KE = 85 \: J[/tex]

The kinetic energy of the object reported to two significant figures is: 85 Joules.

Given the following data:

To find the kinetic energy of the object:

Kinetic energy refers to an energy that is possessed by a physical object or body due to its motion.

Mathematically, kinetic energy is calculated by using the formula;

[tex]K.E = \frac{1}{2} MV^2[/tex]

Where:

Substituting the parameters into the formula, we have;

[tex]K.E = \frac{1}{2}[/tex] × [tex]6.8[/tex] × [tex]5^2[/tex]

[tex]K.E = 3.4[/tex] × [tex]25[/tex]

Kinetic energy = 85 Joules.

Therefore, the kinetic energy of the object is 85 Joules.

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Answer:

a) The magnitude of the friction force is 55.851 newtons, b) The speed of the crate when it reaches the bottom of the ramp is 2.526 meters per second.

Explanation:

a) This situation can be modelled by the Principle of Energy Conservation and the Work-Energy Theorem, where friction represents the only non-conservative force exerting on the crate in motion. Let consider the bottom of the straight ramp as the zero point. The energy equation for the crate is:

[tex]U_{g,1}+K_{1} = U_{g,2}+K_{2}+ W_{fr}[/tex]

Where:

[tex]U_{g,1}[/tex], [tex]U_{g,2}[/tex] - Initial and final gravitational potential energy, measured in joules.

[tex]K_{1}[/tex], [tex]K_{2}[/tex] - Initial and final translational kinetic energy, measured in joules.

[tex]W_{fr}[/tex] - Work losses due to friction, measured in joules.

By applying the defintions of translational kinetic and gravitational potential energies and work, this expression is now expanded:

[tex]m\cdot g \cdot y_{1} + \frac{1}{2}\cdot m\cdot v_{1}^{2} = m\cdot g \cdot y_{2} + \frac{1}{2}\cdot m\cdot v_{2}^{2} + \mu_{k}\cdot m \cdot g \cdot \cos \theta[/tex]

Where:

[tex]m[/tex] - Mass of the crate, measured in kilograms.

[tex]g[/tex] - Gravitational acceleration, measured in meters per square second.

[tex]y_{1}[/tex], [tex]y_{2}[/tex] - Initial and final height of the crate, measured in meters.

[tex]v_{1}[/tex], [tex]v_{2}[/tex] - Initial and final speeds of the crate, measured in meters per second.

[tex]\mu_{k}[/tex] - Kinetic coefficient of friction, dimensionless.

[tex]\theta[/tex] - Ramp inclination, measured in sexagesimal degrees.

The equation is now simplified and the coefficient of friction is consequently cleared:

[tex]y_{1}-y_{2}+\frac{1}{2\cdot g}\cdot (v_{1}^{2}-v_{2}^{2}) = \mu_{k}\cdot \cos \theta[/tex]

[tex]\mu_{k} = \frac{1}{\cos \theta} \cdot \left[y_{1}-y_{2}+\frac{1}{2\cdot g}\cdot (v_{1}^{2}-v_{2}^{2}) \right][/tex]

The final height of the crate is:

[tex]y_{2} = (1.6\,m)\cdot \sin 30^{\circ}[/tex]

[tex]y_{2} = 0.8\,m[/tex]

If [tex]\theta = 30^{\circ}[/tex], [tex]y_{1} = 0\,m[/tex], [tex]y_{2} = 0.8\,m[/tex], [tex]g = 9.807\,\frac{m}{s^{2}}[/tex], [tex]v_{1} = 5\,\frac{m}{s}[/tex] and [tex]v_{2} = 0\,\frac{m}{s}[/tex], the coefficient of friction is:

[tex]\mu_{k} = \frac{1}{\cos 30^{\circ}}\cdot \left\{0\,m-0.8\,m+\frac{1}{2\cdot \left(9.807\,\frac{m}{s^{2}} \right)}\cdot \left[\left(5\,\frac{m}{s} \right)^{2}-\left(0\,\frac{m}{s} \right)^{2}\right] \right\}[/tex]

[tex]\mu_{k} \approx 0.548[/tex]

Then, the magnitude of the friction force is:

[tex]f =\mu_{k}\cdot m\cdot g \cdot \cos \theta[/tex]

If [tex]\mu_{k} \approx 0.548[/tex], [tex]m = 12\,kg[/tex], [tex]g = 9.807\,\frac{m}{s^{2}}[/tex] and [tex]\theta = 30^{\circ}[/tex], the magnitude of the force of friction is:

[tex]f = (0.548)\cdot (12\,kg)\cdot \left(9.807\,\frac{m}{s^{2}} \right)\cdot \cos 30^{\circ}[/tex]

[tex]f = 55.851\,N[/tex]

The magnitude of the force of friction is 55.851 newtons.

b) The energy equation of the situation is:

[tex]m\cdot g \cdot y_{1} + \frac{1}{2}\cdot m\cdot v_{1}^{2} = m\cdot g \cdot y_{2} + \frac{1}{2}\cdot m\cdot v_{2}^{2} + \mu_{k}\cdot m \cdot g \cdot \cos \theta[/tex]

[tex]y_{1}+\frac{1}{2\cdot g}\cdot v_{1}^{2} =y_{2} + \frac{1}{2\cdot g}\cdot v_{2}^{2} + \mu_{k}\cdot \cos \theta[/tex]

Now, the final speed is cleared:

[tex]y_{1}-y_{2}+ \frac{1}{2\cdot g}\cdot v_{1}^{2} -\mu_{k}\cdot \cos \theta= \frac{1}{2\cdot g}\cdot v_{2}^{2}[/tex]

[tex]2\cdot g \cdot (y_{1}-y_{2}-\mu_{k}\cdot \cos \theta) + v_{1}^{2} = v_{2}^{2}[/tex]

[tex]v_{2} = \sqrt{2\cdot g \cdot (y_{1}-y_{2}-\mu_{k}\cdot \cos \theta)+v_{1}^{2}}[/tex]

Given that [tex]g = 9.807\,\frac{m}{s^{2}}[/tex], [tex]y_{1} = 0.8\,m[/tex], [tex]y_{2} = 0\,m[/tex], [tex]\mu_{k} \approx 0.548[/tex], [tex]\theta = 30^{\circ}[/tex] and [tex]v_{1} = 0\,\frac{m}{s}[/tex], the speed of the crate at the bottom of the ramp is:

[tex]v_{2}=\sqrt{2\cdot \left(9.807\,\frac{m}{s^{2}} \right)\cdot [0.8\,m-0\,m-(0.548)\cdot \cos 30^{\circ}]+\left(0\,\frac{m}{s} \right)^{2}}[/tex]

[tex]v_{2}\approx 2.526\,\frac{m}{s}[/tex]

The speed of the crate when it reaches the bottom of the ramp is 2.526 meters per second.

Answer:

[tex]\Delta \theta = 3116.11\,rad[/tex] and [tex]\Delta \theta = 495.944\,rev[/tex]

Explanation:

The tub rotates at constant speed and the kinematic formula to describe the change in angular displacement ([tex]\Delta \theta[/tex]), measured in radians, is:

[tex]\Delta \theta = \omega \cdot \Delta t[/tex]

Where:

[tex]\omega[/tex] - Steady angular speed, measured in radians per second.

[tex]\Delta t[/tex] - Time, measured in seconds.

If [tex]\omega = 31.7\,\frac{rad}{s}[/tex] and [tex]\Delta t = 98.3\,s[/tex], then:

[tex]\Delta \theta = \left(31.7\,\frac{rad}{s} \right)\cdot (98.3\,s)[/tex]

[tex]\Delta \theta = 3116.11\,rad[/tex]

The change in angular displacement, measured in revolutions, is given by the following expression:

[tex]\Delta \theta = (3116.11\,rad)\cdot \left(\frac{1}{2\pi} \frac{rev}{rad} \right)[/tex]

[tex]\Delta \theta = 495.944\,rev[/tex]

Answer:

The water takes longer, because it is the better insulator here.

Explanation:

Conductors and insulators work similarly in "reverse".

If something is a good heat conductor, then it's good at both absorbing heat energy and giving it away. Insulators are good at resisting temperature changes, but also take longer to cool down once they are heated up.

So because copper is the better conductor here, it will cool faster than the water at the same temperature.

Answer:

Matter's resistance to a change in motion is called INERTIA and is directly proportional to the mass of an object.

Explanation:

Answer:

The correct answer is 500 N

Explanation:

This is an exercise in Newton's third law or law of action and reaction

The Earth exerts a force on the person, which we call a weight of 500 N directed downwards, we can call this action and the person exerts a force on the Earth of equal magnitude 500N and in the opposite direction, that is directed upwards.

Which force we call action does not matter, the analysis and conclusions are the same

The correct answer is 500N

Answer:

 object distance  p = 13.33 cm

Explanation:

For this problem of finding the image of an object we must use the constructor equation

         1 / f = 1 / p + 1 / q

where f is the focal length, p and q are the distances to the object and the image, respectively.

In this case they indicate the focal length f = 10 cm, since the person has hyperopia, the image must be formed q = 40 cm, let's find where the object is (p)

        1 / p = 1 / f - 1 / q

        1 / p = 1/10 - 1/40

        1 / p = 0.075

        p = 13.33 cm

Complete question:

a 2.0 kg block slides on the horizontal, frictionless surface until it counters a spring with force constant of  955 N/m. The block comes to rest after compressing the spring a distance of 4.6 cm. Find the initial speed (in m/s) of the block.

Answer:

The initial speed of the block is 1.422 m/s

Explanation:

Given;

mass of the block, m = 2.0 kg

force constant of the spring, K = 955 N/m

compression of the spring, x = 4.6 cm = 0.046 m

Apply Hook's law to determine applied force on the spring;

F = Kx

F = (955 N/m)(0.046 m)

F = 43.93 N

Apply Newton's 2nd law to determine the magnitude of deceleration of the block when it encounters the spring;

F = ma

a = F / m

a = 43.93 / 2

a = 21.965 m/s²

Apply kinematic equation to determine the initial speed of the block;

v² = u² + 2ax

where;

v is the final speed of the block = 0

u is the initial speed of the block

x is the distance traveled by the block = compression of the spring

a is the block deceleration = -21.965 m/s²

0 = u² + 2(-21.965 )(0.046)

0 = u²  - 2.021

u² =  2.021

u = √2.021

u = 1.422 m/s

Therefore, the initial speed of the block is 1.422 m/s

Answer:   The volume of the block will be [tex]100cm^3[/tex]

Explanation:

Density is defined as the mass contained per unit volume.

[tex]Density=\frac{mass}{volume}[/tex]

Given : Mass of cube = 100 grams

Density of cube = [tex]1g/cm^3[/tex]

Putting in the values we get:

[tex]Volume=\frac{mass}{density}[/tex]

[tex]Volume=\frac{100g}{1g/cm^3}=100cm^3[/tex]

 Thus volume of the block will be [tex]100cm^3[/tex]

Answer:

a)  Em = Pe = 4.9 10⁴ J,  b)   K = 2.05 10⁴ J , c)     K = 3.92  104 J ,

e)  W_ friction = Em = 4.9 10⁴ J  

Explanation:

The skier goes down the slope if we assume that there is no friction, the mechanical energy is conserved

         Em = PE + K

where the potential energy is

         PE = m g h

the kinetic energy is

         K = ½ m v²

Let's write the mechanical energy at various points

a) Point A. It is the highest point of the entire system and as the skier is leaving his speed is zero

           Em = Pe

           Em = m g h

let's calculate

           Em = 50 9.8 100

           Em = 4.9 10⁴ J

b) Point B. This point is 60 m

          Em = Pe + K

          K = Em - Pe

          K = 4.9 10⁴ - m g h_B

          K = 4.9   10⁴ - 5 9.8 60

          K = 4.9 10⁴ - 2.85 10⁴

          K = 2.05 10⁴ J

c) point c. This point is 20 m

          Em = Pe + K

          K = Em -Pe = 4.9 10⁴ J - m g h_c

          K = 4.9 10⁴ - 50 9.8 20  = 4.9 10⁴ -  9800

          K = 3.92  104 J

d) point d. It is at a height of 60 m

           Em = Pe + K

           K = Em -Pe

           K = 4.9 10⁴ - m g h

           K = 4.9 10⁴ - 50 9.8 60 =4.9 104 - 2.94 10⁻⁴

           K = 4.897 104 J

e) point E. In this part they indicate that the body is stopped, therefore in this flat part it must be friction so that a device work is carried out that makes the understanding transform into heat by friction and the system stops

            W_ friction = Em = 4.9 10⁴ J

Answer: Speed = [tex]3.10^{-31}[/tex] m/s

Explanation: Like in classical physics, when external net force is zero, relativistic momentum is conserved, i.e.:

[tex]p_{f} = p_{i}[/tex]

Relativistic momentum is calculated as:

p = [tex]\frac{mu}{\sqrt{1-\frac{u^{2}}{c^{2}} } }[/tex]

where:

m is rest mass

u is velocity relative to an observer

c is light speed, which is constant (c=[tex]3.10^{8}[/tex]m/s)

Initial momentum is zero, then:

[tex]p_{f}[/tex] = 0

[tex]p_{1}-p_{2}[/tex] = 0

[tex]p_{1} = p_{2}[/tex]

To find speed of the heavier fragment:

[tex]\frac{mu_{1}}{\sqrt{1-\frac{u^{2}_{1}}{c^{2}} } }=\frac{mu_{2}}{\sqrt{1-\frac{u^{2}_{2}}{c^{2}} } }[/tex]

[tex]\frac{1.86.10^{-27}u_{1}}{\sqrt{1-\frac{u^{2}_{1}}{(3.10^{8})^{2}} } }=\frac{3.10^{-28}.0.844.3.10^{8}}{\sqrt{1-\frac{(0.844c)^{2}}{c^{2}} } }[/tex]

[tex]\frac{1.86.10^{-27}u_{1}}{\sqrt{1-\frac{u^{2}_{1}}{(3.10^{8})^{2}} } }=1.42.10^{-19}[/tex]

[tex]1.86.10^{-27}u_{1} = 1.42.10^{-19}.{\sqrt{1-\frac{u^{2}_{1}}{(3.10^{8})^{2}} } }[/tex]

[tex](1.86.10^{-27}u_{1})^{2} = (1.42.10^{-19}.{\sqrt{1-\frac{u^{2}_{1}}{(3.10^{8})^{2}} } })^{2}[/tex]

[tex]3.46.10^{-54}.u_{1}^{2} = 2.02.10^{-38}.(1-\frac{u_{1}^{2}}{9.10^{16}} )[/tex]

[tex]3.46.10^{-54}.u_{1}^{2} = 2.02.10^{-38} -[2.02.10^{-38}(\frac{u_{1}^{2}}{9.10^{16}} )][/tex]

[tex]3.46.10^{-54}.u_{1}^{2} = 2.02.10^{-38} -2.24.10^{-23}.u^{2}_{1}[/tex]

[tex]3.46.10^{-54}.u_{1}^{2}+2.24.10^{-23}.u^{2}_{1} = 2.02.10^{-38}[/tex]

[tex]2.24.10^{-23}.u^{2}_{1} = 2.02.10^{-38}[/tex]

[tex]u^{2}_{1} = \frac{2.02.10^{-38}}{2.24.10^{-23}}[/tex]

[tex]u_{1} = \sqrt{9.02.10^{-62}}[/tex]

[tex]u_{1} = 3.10^{-31}[/tex]

The speed of the heavier fragment is [tex]u_{1} = 3.10^{-31}[/tex]m/s.

Answer:

Upper plate Q/3

Lower plate 2Q/3

Explanation:

See attached file