When a cube is inscribed in a sphere of radius r, the length Lof a side of the cube is . If a positive point charge Qis placed at the center of the spherical surface, the ratio of the electric flux sphereat the spherical surface to the flux cubeat the surface of the cube is(sphere / cube)

Answer:

Explanation:

Given the simultaneous equation,

3C+4D=5  .............. 1

2C+5D=2 ............... 2

Solving for the value of C and D using substitution method.

From equation 1;

3C = 5-4D

Divide both sides by 3

3C/3 =  (5-4D)/3

C = (5-4D)/3 .... 3

From equation 2:

2C+5D=2

5D = 2-2C

Divide both sides by 5;

5D/5 = 2-2C/5

D = (2-2C)/5 ..... 4

Substitute equation 4 into 3;

C = 5-4{(2-2C)/5}/3

C = [5 - (8-8C/5)]/3

C = [25-(8-8C)/5]/3

C = (17+8C)/15

15C = 17+8C

15C-8C = 17

7C = 17

C = 17/7

Substitute C = 17/7 into equation 4 to get the value of D

D = (2-2(17/7))/5

D = (2-34/7)/5

D = 14-34/35

D = -20/35

D = -4/7

Hence the value of C = 17/7, D = -4/7

Answer:

  y/y₀ = 1/2 + v₀²/(2 g y₀)

Explanation:

         This in a kinematics exercise in a mention  

ball A.  

Since the ball is dropped, its velocity starts at zero, at the meeting point the equation is  

[tex]v_{A}^2[/tex]= - 2 g (y₀-y)  

ball B  

v_{B}^2 = v₀² - 2 g y

we substitute  

               2v_{B}^2 = -2 g (y₀ -y)  

               v_{B}^2 = - g y₀ + 2g y  

              v_{B}^2 = v₀² - 2gy

we have a system of two equations with two unknowns, therefore it can be solved. Let's multiply-by -1 and add  

       0 = g y₀ + v₀² -2gy  

we clear the height  

      y = (g yo + v₀²) / 2g  

     y = yo / 2 + v₀² / 2g

In this exercise we assume that the height of the building is known and the initial velocity of ball B  

The fraction is

y/yo = 1/2 + v₀²/(2gyo)

Answer:

The speed of the car just before braking is 23.66 m/s.

Explanation:

Given;

mark of the skid, d = 80 m

deceleration of the car, a = 3.5 m/s²

To determine the speed of the car just before braking, we apply the following kinematic equation;

[tex]v^2 = u^2 + 2ad\\\\v^2 = 0 + 2(3.5)(80)\\\\v^2 = 560\\\\v= \sqrt{560}\\\\v = 23.66 \ m/s[/tex]

Therefore, the speed of the car just before braking is 23.66 m/s.

Explanation:

Assuming constant speed:

Distance = speed × time

17.8 m = (5.3 m/s) t

t = 3.36 s

Answer:

The pressure is [tex]P_2 = 1.84 \ a.t.m[/tex]

Explanation:

From the question we are told that

   The first  volume of  is  [tex]v_1 = 3.5 \ L[/tex]

   The first  pressure is  [tex]P_1 = 2.7 \ a.t.m[/tex]

   The first  temperature is  [tex]T_1 = 350 \ K[/tex]

    The  new temperature is  [tex]T_2 = 620 \ K[/tex]

     The  new volume is  [tex]V_2 = 9.1 \ a.t.m[/tex]

Generally according to the combined gas law we have that

      [tex]\frac{P_1 V_1 }{T_1 } = \frac{P_2 V_2 }{T_2 }[/tex]

=>  [tex]P_2 = \frac{P_1 * V_1 * T_2 }{T_1 * V_2 }[/tex]

=>    [tex]P_2 = \frac{ 2.7 * 3.5 * 620 }{ 350 * 9.1 }[/tex]

=>  [tex]P_2 = 1.84 \ a.t.m[/tex]

Answer:

D

Explanation:

pressure change have nothing to do with the spontaneity.

Entropy change , enthalpy change , temperature have roles in deciding spontaneity.

Answer

a)0.0495 J

b)0.01681 m

c)0.7218 m/s

Explanation:

Given

Mass of the.toy M = 0.190 kg

force constant k = 350 N/m

Displacement from equilibrium x = 0.0140 m

Speed v = 0.400 m/s

a)What is the toy's total energy at any point of its motion?

The total energy at any point of it's motion can be calculated by adding together both the potential and kinetic energy of the toy, since it's posses potential energy when at rest and kinetic energy at motion

Total energy E = kinetic energy + potential energy

E = ¹/₂mv² + ¹/₂kx²

E = ¹/₂ (0.190)(0.4)² + ¹/₂ (350)(0.0140)²

E = 0.0495 J

Hence,the total energy is 0.0495 J

b) the amplitude of the motion can be calculated using below formula

Let amplitude = A

E = ¹/₂KA²

if we make Amplitude A the subject of the formula we have

A=√(2E/k)

But we have calculated our E up there, our K was given in question then if we substitute we have

A= √(2×0.0495)/350

Ans: 0.01681 m

Hence, our Amplitude is 0.01681 m

c) the the toy's maximum speed during its motion can be calculated using the expression below

Let maximum speed = vmax

E = (1/2)M * vmax^2

If we make vmax the subject of the formula we have

vmax =√(2E/m)

vmax= √(2×0.0495)/0.190

vmax=0.7218 m/s

Hence our vmax is 0.7218 m/s

Answer:

a) A = 4.0 m , b)   w = 3.0 rad / s , c)  f = 0.477 Hz , d) T = 20.94 s

Explanation:

The equation that describes the oscillatory motion is

          x = A cos (wt + fi)

In the exercise we are told that the expression is

          x = 4.0 cos (3.0 t + 0.10)

let's answer the different questions

a) the amplitude is

         A = 4.0 m

b) the frequency or angular velocity

         w = 3.0 rad / s

c) angular velocity and frequency are related

          w = 2π f

           f = w / 2π

           f = 3 / 2π

           f = 0.477 Hz

d) the period

frequency and period are related

           T = 1 / f

           T = 1 / 0.477

           T = 20.94 s

e) the phase constant

          Ф = 0.10 rad

f) velocity is defined by

          v = dx / dt

         v = - A w sin (wt + Ф)

speed is maximum when sine is + -1

         v = A w

          v = 4 3

          v = 12 m / s

g) the angular velocity is

          w² = k / m

          k = m w²

          k = 1.2 3²

          k = 10.8 N / m

h) the total energy of the oscillator is

          Em = ½ k A²

           Em = ½ 10.8 4²

          Em = 43.2 J

i) the potential energy is

           Ke = ½ k x²

for t = 0 x = 4 cos (0 + 0.1)

               x = 3.98 m

j) kinetic energy

           K = ½ m v²

for t = 00.1 ²

    v = A w sin 0.10

    v = 4 3 sin 0.10

    v = 1.98 m / s

Answer:

Therefore, the brick appears to have an additional force pushing it upward.

Explanation:

When a brick is submerged in the water, it has two forces acting upon it. One force is the gravitational force or the weight of the brick, that acts downward. The weight force also acts on the brick when it is not in water. But, in water an additional force acts on the brick. This additional force is named as Buoyant Force. This force is equal to the weight of the water displaced by the brick. And this Buoyant Force acts on the brick in the upward direction. The formula for this force is given as follows:

Buoyant Force = (Density of Water)(Volume of Water Displaced)(g)

Therefore, the brick appears to have an additional force pushing it upward.

Answer and Explanation: When tossing a ball up in the air, the forces acting on the ball are due to Gravity, which is defined by gravitational acceleration on that location on Earth (approximately 9.8 m/s²) multiplied by mass of the ball; Force of thrown, i.e., the force you threw the ball and air resistance force, which is proportional to the square of the ball's through the air and the ball's cross section area. To facilite calculations, air resistance force is normally ignored.

Answer:

weight and drag

Explanation:

Explanation:

The total displacement is 3 miles

What is displacement?

Simply put it is the sum total of the changes in position of an object from it initial position to it final position, It is a vector quantity and has a direction and magnitude.

In our example the displacement the total points of movement can be annotated as

From A to B to C

From A to B= 1 mile

From B to C= 1 miles

Displacement is 1 + 2= 3 miles

Answer:

C) three

Explanation:

Let gram of gold required be m . Let temperature change in both be Δ t .

heat absorbed = mass x specific heat x change in temperature

for copper

heat absorbed = 1 x .385 x Δt

for gold

heat absorbed = m x .129 x Δt

So

m x .129 x Δt = 1 x .385 x Δt

m = 2.98

= 3 g approximately .

Answer:

Energy will be reduced by 0.3

Explanation:

Given that E = 1/2 QV

So if V is increased by 6

=> V = E/ 3Q

So the energy will be divided by a factor 1/3 of be reduced by 0.3

Answer:

The  value is  [tex]\mu_k = 0.102 0[/tex]

Explanation:

From the question we are told that

    The initial speed is  [tex]u = 10 \ m/s[/tex]

    The  distance traveled is  [tex]d = 50 \ m[/tex]

Generally we can obtain the acceleration using the kinetic equation as follows

     [tex]v^2 = u^2 + 2as[/tex]

=>   [tex]a = \frac{v^2 - u^2 }{ 2s}[/tex]

=>   [tex]a = \frac{0^2 - 10^2 }{ 2 * 50 }[/tex]

=>   [tex]a = -1 m/s^2[/tex]

The  negative sign shows that the pluck is decelerating

  The force driving the pluck is mathematically evaluated as

       [tex]F = ma[/tex]

 This force is also equivalent to the frictional force acting on the pluck

So  

      [tex]ma = m * g* \mu_k[/tex]

=>  [tex]\mu_k = \frac{a}{g}[/tex]

=>   [tex]\mu_k = \frac{1}{9.8 }[/tex]

=>   [tex]\mu_k = 0.102 0[/tex]

Answer:

T = 0

Explanation:

Given that,

Mass of the box, m = 55 kg

We need to find the tension in the rope if the box is at rest. When the object is at rest, its acceleration is equal to 0. It would mean that the net force equals 0. So, the tension in the rope is equal to 0.

Answer:

The height of the object is 50 feet

Explanation:

Given that:

The path of an object projected at a 45 degree angle with initial velocity of 80 feet per second is given by the  function  [tex]h (x) =\dfrac{-32}{(80)^2}x^2+x[/tex]

where;

x  is the horizontal distance traveled and  h(x) is the height in feet.

The objective is to use the TRACE feature of your calculator to determine the height of the object when it has traveled 100 feet away horizontally.

Before then;

If the function [tex]h (x) =\dfrac{-32}{(80)^2}x^2+x[/tex]

and x = 100

then :

[tex]h (x) =\dfrac{-32}{(80)^2}(100)^2+100[/tex]

[tex]h (x) =\dfrac{-32}{6400} \times 10000+100[/tex]

[tex]h (x) =- 0.005 \times 10000+100[/tex]

[tex]h (x) =- 50+100[/tex]

h(x) = 50 feet

Using the TRACE CALCULATOR,

In your Trace calculator;

input Y = X - 32 X^2/(80)        this  because in the calculator Y denotes h(x)

Now over to the WINDOW

set the window as follows:

Xmin = 0

Xmax = 200

Xsc1 =1

Ymin = 0

Ymax = 50

Ysc = 1

Xres = 1

After that, click on the graph key and an output will display as seen in the image below.

Therefore, the show the value of Y which we earlier said it denotes the h(x) = 50 feet

Answer:

a) 0.22 m/s

b) 531.67 N

c) 508.81 J

d) 38.72 J

Explanation:

the mass of the astronaut = 121 kg

astronaut's push of speed = 2.9 m/s

mass of the space capsule = 1600 kg

a) according to the conservation of momentum, the summation of the total momentum in a system must be equal to zero.

let us take the direction of the astronaut as positive.

Astronaut's momentum p = mv

where

m is the mass

v is the velocity

momentum p = 121 x 2.9 = 350.9 kg-m/s

The space capsules momentum = mv

==> 1600 x (-v) = -1600v    this is because the space capsule moves in the opposite direction to the astronaut.

according to conservation of momentum

350.9 + (-1600v) = 0

350.9 = 1600v

v = 350.9/1600 = 0.22 m/s

b) magnitude of the force F is the rate of change of momentum.

The astronaut and the space capsule both change momentum from 0 to 350.9 kg-m/s. In 0.66 seconds, the force will be

F = [tex]\frac{m(v - u)}{t}[/tex]

where

u is their initial velocity = 0 m/s

where v = 2.9

t = 0.66

substituting, we have

F = [tex]\frac{121(2.9 - 0)}{0.66}[/tex] = 350.9/0.66 = 531.67 N  this same force is experienced by the space capsule

c) Kinetic energy of the astronaut = [tex]\frac{1}{2} mv^{2}[/tex]

m is the mass = 121 kg

v is the velocity = 2.9 m/s

KE = [tex]\frac{1}{2}*121*2.9^{2}[/tex] = 508.81 J

d) Kinetic energy of the space capsule = [tex]\frac{1}{2} mv^{2}[/tex]

KE = [tex]\frac{1}{2}* 1600* 0.22^{2}[/tex] = 38.72 J

Answer:

A. The fan does work on the air in the room leading to an increase in its thermal energy and temperature.

Explanation:

Fans move fluid, typically a gas, such as air, through a room or an enclosure. A fan consists of a rotating arrangement of vanes or blades (impeller), which acts on the air. The action of the impeller does work on the fan by compressing and moving the air forward, doing work on it in the process. The work done on the fan leads to an increase in the thermal energy of the air.

Answer:

In this process, the pressure increases by a factor of 2.

Explanation:

For an isothermal process, the temperature remains constant throughout the process.

Also, PV = constant

It means that there is an inverse relationship between pressure and volume of the gas.

If the volume is decreased by a factor of 2, the pressure increases by a factor of 2. Hence, the correct option is (c).

This question is incomplete, the complete question is;

When an auditorium has a solid wall, sound waves will tend to perfectly reflect off the wall (i.e. with a 180o phase change). If listening to music, as from an orchestra, the incoming and reflected waves will interfere with each other. For a listener sitting 0.5 m from the wall, what is the lowest frequency which gets suppressed by this interference? Use vsound=330 m/s.

Answer: f = 165 Hz

the lowest frequency which gets suppressed by this interference is 165 Hz

Explanation:

For a reflected wave (out of phase), the path difference between the incoming and reflected wave should be equal to the half integral multiple of wavelength.

r₂ - r₁ = ( m + 1/2) λ/2

r₂ is the distance from the source to observer via reflection

r₁ is distance from source to observer

here r₂ would travel an additional distance of 0.5 m due to reflection that straight approaching wave.

Therefor to have minimum/lowest possible frequency, we say m = 0

we substitute

0.5 = ( 0 + 1/2 ) λ/2

λ = 2m

The frequency would be

f = Vsound / λ

f = 330 / 2

f = 165 Hz

Therefore the lowest frequency which gets suppressed by this interference is 165 Hz

Answer:

λ = 2.7608 x 10⁻⁷ m = 276.08 nm

Explanation:

The work function of a metallic surface is the minimum amount of photon energy required to release the photo-electrons from the surface of metal. The work function is given by the following formula:

Work Function = hc/λ

where,

Work Function = (4.5 eV)(1.6 x 10⁻¹⁹ J/1 eV) = 7.2 x 10⁻¹⁹ J

h = Plank's Constant = 6.626 x 10⁻³⁴ J.s

c = speed of light = 3 x 10⁸ m/s

λ = longest wavelength capable of releasing electron.

Therefore,

7.2 x 10⁻¹⁹ J = (6.626 x 10⁻³⁴ J.s)(3 x 10⁸ m/s)/λ

λ = (6.626 x 10⁻³⁴ J.s)(3 x 10⁸ m/s)/(7.2 x 10⁻¹⁹ J)

λ = 2.7608 x 10⁻⁷ m = 276.08 nm

Answer:

[tex] \boxed{\sf Kinetic \ energy \ (KE) = 48 \ J} [/tex]

Given:

Mass (m) = 6 kg

Speed (v) = 4 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 \times {4}^{2} [/tex]

[tex] \sf \implies KE = \frac{1}{ \cancel{2}} \times \cancel{2} \times 3 \times 16[/tex]

[tex] \sf \implies KE =3 \times 16[/tex]

[tex] \sf \implies KE = 48 \: J[/tex]

Answer:

0.2871 kg m/s

Explanation:

p = mv

convert 33g into kg (0.033)

mulitply byt 8.7 to get 0.2871

Answer:

increase the tension on the hose and shake the end fewer times per second.

Explanation:

This is because Tension of the rope is directly proportional to wavelength and inversely proportional to the frequency ( shakes per second) so increasing tension increases wavelength and vice versa

Wavelength= Tension/ frequency

The most efficient way for her to increase the wavelength is to increase the rate of shaking the rope per second.

Wavelength measures the distance of wave that occur between one crest and another crest.

To increase the wavelength the rope end should be shaked in a number of time per second this will help build up tension in the rope.

Therefore, she should increase the rate of shaking the rope per second.

Learn more on wavelength here,

https://brainly.com/question/10750459

Answer:

The  work function is  [tex]\phi = 2.46 \ eV[/tex]

Explanation:

From the question we are told that

    The light energy is  [tex]E = 3.56 eV[/tex]

     The  stopping voltage is  [tex]V = 1.10 \ V[/tex]

Generally work function is mathematically represented as

      [tex]\phi = E - KE[/tex]

Where KE is the kinetic energy of the ejected electron and it is mathematically represented as

         [tex]KE = V * e[/tex]

Where  e is the charge on the electron

So  

        [tex]KE = 1.10eV[/tex]

Thus  

        [tex]\phi = 3.56eV - 1.10 eV[/tex]

=>      [tex]\phi = 2.46 \ eV[/tex]

Answer:

The pressure on the wall is 9416.25 N/m²

Explanation:

Please see the attachments below

Answer:A is the correct answer

Explanation:

Answer:

The work done to lift the counterweight equals the potential energy acquired

Explanation:

since this is vertically applied force on the counterweight, and the distance the force is displacing the counterweight is in the same direction as the applied force, it equals the gained potential energy

Answer:

The velocity is  [tex]v_x = 0.356 \ m/s[/tex]

Explanation:

From the question we are told that

   The  mass is  [tex]m = 1.10 \ kg[/tex]

   The  spring constant is  [tex]k = 18 \ N/m[/tex]

   The  speed is [tex]v = 40 \ cm / s = 0.4 m/s[/tex]

    The  position considered is  x =  0.45 A  

Here A is the amplitude which is mathematically represented as

     [tex]A = v * \sqrt{\frac{m}{k} }[/tex]

=>     [tex]A = 0.4 * \sqrt{\frac{1.10}{18 } }[/tex]

=>     [tex]A = 0.0989 \ m[/tex]

So     [tex]x = 0.45 * 0.0989[/tex]

=>     [tex]x = 0.045 \ m[/tex]

Generally the speed at  x  is mathematically represented as

      [tex]v_x = \sqrt{ \frac{k}{m} * [A^2 - x^2 ]}[/tex]

=>    [tex]v_x = \sqrt{ \frac{18}{ 1.10} * [0.0989^2 - 0.045^2 ]}[/tex]

=>    [tex]v_x = 0.356 \ m/s[/tex]

Answer:

 λ =365.4 nm

Explanation:

Boh's atomic model of the Hydrogen atom the energy of each level is

        Eₙ = - 13.606 / n²

where the synergy is in electonvotes and the value of E₀ = 13.606 eV is the energy of the base state of hydrogen.

An atomic transition occurs when an electron goes from an excited state and joins everything of lower energy.

                 ED = 13.606 (1 / n₀² - 1 /[tex]n_{f}^{2}[/tex])

we are going to apply this relationship to answer slash.

At the beginning of the studies of atomic transitions, each group did not consider having a different name

name        Initial state

Lymman         1

Balmer           2

the final state is any other state sta the continuum that corresponds to n = inf

Let's look for the highest energy of the Balmer series

              ΔE = 13.606 (1/2² - 1 /∞)

              ΔE = 3.4015 eV

Let's use the Planck relation for the energy

                E = h f = h c /λ

                λ = h c / E

Let's reduce the energy to J

              E = 3.4015 eV (1.6 10⁻¹⁹ J / 1 eV) = 5.4424 10⁻¹⁹

            λ = 6.63 10⁻³⁴  3 10⁸ / 5.4424 10⁻¹⁹

            λ = 3.654 10⁻⁷ m

            λ = 3,654 10⁻⁷ m (10⁹ nm / 1m)

            λ =365.4 nm

this eta radiation in the ultraviolet range