Suppose the sediment density (g/cm) of a randomly selected specimen from a certain region is normally distributed with mean 2.61 and standard deviation 0.82. (a) If a random sample of 25 specimens is selected, what is the probability that the sample average sediment density is at most 3.00? Between 2.61 and 3.00

Answer:

The average force exerted on the bullet are of F=9000 Newtons.

Explanation:

t= 2*10⁻³ s

m= 0.03 kg

V= 600 m/s

F*t= m*V

F= (m*V)/t

F= 9000 N

The average force exerted on the bullet to accelerate it to a speed of 600 m/s in a time of 2.00 ms is 9000 Newtons (N). when a bullet is accelerated down the barrel of a gun by hot gases produced in the combustion of gunpowder.

Given:

Mass of the bullet (m) = 0.0300 kg

The final velocity of the bullet (v) = 600 m/s

Time taken to reach the final velocity (t) = 2.00 ms = 2.00 × 10⁻³ s

acceleration (a) = (change in velocity) / (time taken)

a = (v - u) / t

a = (600 - 0 ) / (2.00 × 10⁻³)

Now, we can calculate the average force using Newton's second law:

force (F) = mass (m) × acceleration (a)

F = 0.0300 × [(600 ) / (2.00 × 10⁻³)]

F = 0.0300× (3.00 × 10⁵)

F = 9000 N

Therefore, the average force exerted on the bullet to accelerate it to a speed of 600 m/s in a time of 2.00 ms is 9000 Newtons (N).

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Answer:

The equilibrium vibrational frequency that causes the shift is [tex]0.56\times10^{14}\ Hz[/tex]

Explanation:

Given that,

Wavelength of Raman line [tex]\lambda'=4768.5\ A[/tex]

Wavelength [tex]\lambda=4358.3\ A[/tex]

We need to calculate the frequency

Using formula of frequency

[tex]f =\dfrac{c}{\lambda}[/tex]

For 4748.5 A

The frequency is

[tex]f'=\dfrac{3\times10^{8}}{4748.5\times10^{-10}}[/tex]

[tex]f' =6.32\times10^{14}\ Hz[/tex]

For 4358.3 A

The frequency is

[tex]f=\dfrac{3\times10^{8}}{4358.3\times10^{-10}}[/tex]

[tex]f=6.88\times10^{14}\ Hz[/tex]

We need to calculate the shift

[tex]\Delta f=f-f'[/tex]

[tex]\Delta f=(6.88-6.32)\times10^{14}\ Hz[/tex]

[tex]\Delta f=0.56\times10^{14}\ Hz[/tex]

Hence, The equilibrium vibrational frequency that causes the shift is [tex]0.56\times10^{14}\ Hz[/tex]

Answer:

The normal force acting on the block is 980 N.

Explanation:

Mass of box = 100 kg

Coefficient of static friction = 0.40

Coefficient of kinetic friction = 0.20

We need to calculate the normal force

We know that,

When the object is placed on the flat surface then the normal force is equal to the weight of the object.

So. The normal force = mass x acceleration due to gravity

[tex]N=mg[/tex]

Where, N = Normal force

m = mass of object

g = acceleration due to gravity

[tex]N=100\times9.8[/tex]

[tex]N=980\ N[/tex]

Hence, The normal force acting on the block is 980 N.

Final answer:

The normal force acts perpendicular to the floor supporting the box and is equal to 980 N.

Explanation:

The question asks about the normal force acting on a 100-kg box at rest on the floor. To find the normal force on the box, we can use the equation that relates the normal force to the weight of the object, which is W = mg, where m is the mass and g is the acceleration due to gravity.

Given that the mass of the box is 100 kg and the acceleration due to gravity is 9.80 m/s², the normal force can be calculated as:

Normal Force (N) = Mass (m) × Acceleration due to gravity (g)

Normal Force = 100 kg × 9.80 m/s² = 980 N

The normal force acts perpendicular to the floor supporting the box and is equal to 980 N. It is often confused with the applied force P, but the normal force is related to the box's weight, not the horizontal force applied.

Answer:

Magnitude of angular acceleration = -3.95 rad/s²

Explanation:

Angular acceleration is the ratio of linear acceleration and radius.

That is

        [tex]\texttt{Angular acceleration}=\frac{\texttt{Linear acceleration}}{\texttt{Radius}}\\\\\alpha =\frac{a}{r}[/tex]

Radius = 72 cm = 0.72 m

Linear acceleration is rate of change of velocity.

[tex]a=\frac{11.7-26.5}{5.2}=-2.85m/s^2[/tex]

Angular acceleration

        [tex]\alpha =\frac{a}{r}=\frac{-2.85}{0.72}=-3.95rad/s^2[/tex]

Angular acceleration = -3.95 rad/s²  

Magnitude =  3.95 rad/s²     

Explanation:

It is given that,

Mass of the metal wire, m = 500 g = 0.5 kg

Tension in the wire, T = 80 N

Length of wire, l = 50 cm = 0.5 m

(a) The speed of the transverse wave is given by :

[tex]v=\sqrt{\dfrac{T}{M}}[/tex]

M is the mass per unit length or M = m/l

[tex]v=\sqrt{\dfrac{T.l}{m}}[/tex]

[tex]v=\sqrt{\dfrac{80\ N\times 0.5\ m}{0.5\ kg}}[/tex]

v = 8.94 m/s

(b) If the wire is cut in half, so l = l/2

[tex]v=\sqrt{\dfrac{T.l}{2m}}[/tex]

[tex]v=\sqrt{\dfrac{80\ N\times 0.5\ m}{2\times 0.5\ kg}}[/tex]

v = 6.32 m/s

Hence, this is the required solution.

Answer:

A) 50.0 g Al

Explanation:

We can calculate the temperature change of each substance by using the equation:

[tex]\Delta T=\frac{Q}{mC_s}[/tex]

where

Q = 200.0 J is the heat provided to the substance

m is the mass of the substance

[tex]C_s[/tex] is the specific heat of the substance

Let's apply the formula for each substance:

A) m = 50.0 g, Cs = 0.903 J/g°C

[tex]\Delta T=\frac{200}{(50)(0.903)}=4.4^{\circ}C[/tex]

B) m = 50.0 g, Cs = 0.385 J/g°C

[tex]\Delta T=\frac{200}{(50)(0.385)}=10.4^{\circ}C[/tex]

C) m = 25.0 g, Cs = 0.79 J/g°C

[tex]\Delta T=\frac{200}{(25)(0.79)}=10.1^{\circ}C[/tex]

D) m = 25.0 g, Cs = 0.128 J/g°C

[tex]\Delta T=\frac{200}{(25)(0.128)}=62.5^{\circ}C[/tex]

E) m = 25.0 g, Cs = 0.235 J/g°C

[tex]\Delta T=\frac{200}{(25)(0.235)}=34.0^{\circ}C[/tex]

As we can see, substance A) (Aluminium) is the one that undergoes the smallest temperature change.

The substance that would show the smallest temperature change upon gaining 200.0 J of heat is Au (Gold), as calculated using the formula for calculating heat (Q = mcΔT) and rearranging for ΔT, then substituting the given values.

The substance that would show the smallest temperature change upon gaining 200.0 J of heat can be determined using the formula used to calculate heat (Q), which is Q = mcΔT, where m is the mass, c is the specific heat capacity, and ΔT is the temperature change. We want to find the smallest temperature change, so we rearrange the equation to solve for ΔT, which gives us ΔT = Q/(mc). By substituting the given values for each substance into this equation, we find that the smallest temperature change is for Au (Gold).

For Au: ΔT = 200.0J / (25.0g x 0.128 J/g°C) = 62.5°C. All other substances have a smaller temperature change when they absorb 200.0J of heat, due to their higher specific heat capacity.

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Answer:

3.08 Nm

Explanation:

N = 200, diameter = 6 cm, radius = 3 cm, I = 7 A, B = 0.90 T, Angle = 30 degree

The angle made with the normal of the coil, theta = 90 - 30 = 60 degree

Torque = N I A B Sin Theta

Torque = 200 x 7 x 3.14 x 0.03 x 0.03 x 0.90 x Sin 60

Torque = 3.08 Nm

Solution:

Let the slope of the best fit line be represented by '[tex]m_{best}[/tex]'

and the slope of the worst fit line be represented by '[tex]m_{worst}[/tex]'

Given that:

[tex]m_{best}[/tex] = 1.35 m/s

[tex]m_{worst}[/tex] = 1.29 m/s

Then the uncertainity in the slope of the line is given by the formula:

[tex]\Delta m = \frac{m_{best}-m_{worst}}{2}[/tex]               (1)

Substituting values in eqn (1), we get

[tex]\Delta m = \frac{1.35 - 1.29}{2}[/tex] = 0.03 m/s

Answer:

[tex]Q = 1.45 \times 10^{-7} C[/tex]

Explanation:

Here flux passing through each surface is given

so total flux through whole cube is given by

[tex]\phi = 2060 + 1590 + 1690 + 3430 + 1870 + 5760[/tex]

[tex]\phi = 16400 Nm^2 C[/tex]

now we also know that total flux through a closed surface depends on the total charge enclosed in the surface

So we will have

[tex]\frac{Q}{\epsilon_0} = 16400[/tex]

[tex]Q = (8.85 \times 10^{-12})(16400)[/tex]

[tex]Q = 1.45 \times 10^{-7} C[/tex]

The total charge [tex](\( Q \))[/tex] enclosed by the rectangular box is approximately [tex]\( 2.544 \times 10^{-4} \, \text{C} \)[/tex].

The electric flux [tex](\( \Phi \))[/tex] through a closed surface is given by Gauss's Law:

[tex]\[ \Phi = \frac{Q}{\varepsilon_0} \][/tex]

where:

- [tex]\( \Phi \)[/tex] is the electric flux,

- [tex]\( Q \)[/tex] is the total charge enclosed by the closed surface,

- [tex]\( \varepsilon_0 \)[/tex] is the permittivity of free space [tex](\( \varepsilon_0 \approx 8.85 \times 10^{-12} \, \text{C}^2/\text{Nm}^2 \))[/tex].

For a closed box, the total electric flux [tex](\( \Phi_{\text{total}} \))[/tex] is the sum of the electric flux through each of its six surfaces. Let's denote the electric flux through each surface as [tex]\( \Phi_i \) where \( i = 1, 2, \ldots, 6 \)[/tex].

[tex]\[ \Phi_{\text{total}} = \sum_{i=1}^{6} \Phi_i \][/tex]

Now, we can set up an equation using the given values:

[tex]\[ \Phi_{\text{total}} = 12060 \, \text{Nm}^2/\text{C} + 1590 \, \text{Nm}^2/\text{C} + 1690 \, \text{Nm}^2/\text{C} + 3430 \, \text{Nm}^2/\text{C} + 1870 \, \text{Nm}^2/\text{C} + 5760 \, \text{Nm}^2/\text{C} \][/tex]

[tex]\[ \Phi_{\text{total}} = 28800 \, \text{Nm}^2/\text{C} \][/tex]

Now, use Gauss's Law to find the total charge [tex](\( Q \))[/tex] enclosed by the closed surface:

[tex]\[ Q = \Phi_{\text{total}} \cdot \varepsilon_0 \][/tex]

[tex]\[ Q = 28800 \, \text{Nm}^2/\text{C} \cdot 8.85 \times 10^{-12} \, \text{C}^2/\text{Nm}^2 \][/tex]

[tex]\[ Q \approx 2.544 \times 10^{-4} \, \text{C} \][/tex]

So, the total charge [tex](\( Q \))[/tex] enclosed by the rectangular box is approximately [tex]\( 2.544 \times 10^{-4} \, \text{C} \)[/tex].

The magnitude of the angular momentum of the paperclip attached to the spinning vinyl record is approximately 0.0033 kg m²/s. This is calculated using the formulas for moment of inertia and angular momentum.

To calculate the angular momentum of the paperclip, we first need to know the moment of inertia (I) of the paperclip. The moment of inertia can be calculated using the formula I = mR² where 'm' is the mass of the paperclip (converted into kg - 0.018 kg) and 'R' is the radius of the record player (converted into m - 0.24 m).

So, I = 0.018 kg * (0.24 m)² = 0.0010368 kg m².

Next, we use the formula for angular momentum (L), which is L = Iω, where ω is the angular velocity. Given ω = 3.2 rad/s, we plug these values into our formula:

L = 0.0010368 kg m² * 3.2 rad/s = t0.00331776 kg m²/s.

Thus, rounding to the nearest ten-thousandth, the magnitude of the angular momentum of the paperclip is 0.0033 kg m²/s.

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The magnitude of the angular momentum of the paper clip is approximately [tex]\( 0.0033 \text{ kg m}^2/\text{s} \)[/tex].

The magnitude of the angular momentum of the paper clip is given by the formula [tex]\( L = I\omega \)[/tex], where I is the moment of inertia of the paper clip and [tex]\( \omega \)[/tex] is the angular velocity of the record.

Given:

- Mass of the paper clip, [tex]\( m = 18 \) g \( = 0.018 \)[/tex] kg (after converting grams to kilograms)

- Diameter of the record, [tex]\( d = 48 \) cm \( = 0.48 \)[/tex] m (after converting centimeters to meters)

- Radius of the record, [tex]\( r = \frac{d}{2} = \frac{0.48}{2} = 0.24 \)[/tex]m

- Angular velocity, [tex]\( \omega = 3.2 \)[/tex] rad/s

Now, we calculate the moment of inertia I:

[tex]\[ I = mr^2 = 0.018 \times (0.24)^2 \] \[ I = 0.018 \times 0.0576 \] \[ I = 0.0010368 \text{ kg m}^2 \][/tex]

Next, we calculate the angular momentum L:

[tex]\[ L = I\omega \] \[ L = 0.0010368 \times 3.2 \] \[ L = 0.00331776 \text{ kg m}^2/\text{s} \][/tex]

Rounding to the nearest ten-thousandth, we get:

[tex]\[ L \approx 0.0033 \text{ kg m}^2/\text{s} \][/tex]

Answer:

The pressure of the remaining gas in the tank is 6.4 atm.

Explanation:

Given that,

Temperature T = 13+273=286 K

Pressure = 10.0 atm

We need to calculate the pressure of the remaining gas

Using equation of ideal gas

[tex]PV=nRT[/tex]

For a gas

[tex]P_{1}V_{1}=nRT_{1}[/tex]

Where, P = pressure

V = volume

T = temperature

Put the value in the equation

[tex]10\times V=nR\times286[/tex]....(I)

When the temperature of the gas is increased

Then,

[tex]P_{2}V_{2}=\dfrac{n}{2}RT_{2}[/tex]....(II)

Divided equation (I) by equation (II)

[tex]\dfrac{P_{1}V}{P_{2}V}=\dfrac{nRT_{1}}{\dfrac{n}{2}RT_{2}}[/tex]

[tex]\dfrac{10\times V}{P_{2}V}=\dfrac{nR\times286}{\dfrac{n}{2}R368}[/tex]

[tex]P_{2}=\dfrac{10\times368}{2\times286}[/tex]

[tex]P_{2}= 6.433\ atm[/tex]

[tex]P_{2}=6.4\ atm[/tex]

Hence, The pressure of the remaining gas in the tank is 6.4 atm.

Answer:

Change in ball's momentum is 1.5 kg-m/s.

Explanation:

It is given that,

Mass of the ball, m = 0.15 kg

Speed before the impact, u = 6.5 m/s

Speed after the impact, v = -3.5 m/s (as it will rebound)

We need to find the change in the magnitude of the ball's momentum. It is given by :

[tex]\Delta p=m(v-u)[/tex]

[tex]\Delta p=0.15\ kg(-3.5\ m/s-6.5\ m/s)[/tex]

[tex]\Delta p=-1.5\ kg-m/s[/tex]

So, the change in the ball's momentum is 1.5 kg-m/s. Hence, this is the required solution.

The change in the magnitude of the ball's momentum is 1.125 kg·m/s.

The change in the magnitude of an object's momentum can be calculated by subtracting its initial momentum from its final momentum. In this case, the initial momentum of the ball is calculated by multiplying its mass (0.15 kg) by its initial speed (6.5 m/s), and the final momentum is calculated by multiplying its mass by its final speed (3.5 m/s).

So, the change in the magnitude of the ball's momentum is calculated as:

|pf| - |pi| = (0.15 kg)(3.5 m/s) - (0.15 kg)(6.5 m/s) = -0.15 kg·m/s - 0.975 kg·m/s = -1.125 kg·m/s.

Since momentum is a vector quantity, the change in its magnitude is given by its absolute value, which is 1.125 kg·m/s. Therefore, the correct answer is A. 1.125 kg·m/s.

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Answer:

Torque, [tex]\tau=0.1669\ N-m[/tex]

Explanation:

It is given that,

Radius of the circular loop, r = 0.7 cm = 0.007 m

Number of turns, N = 520

Current in the loop, I = 3.9 A

The axis of the loop makes an angle of 57 degrees with a magnetic field.

Magnetic field, B = 0.982 T

We need to find the magnitude of torque on the loop. It is given by :

[tex]\tau=\mu\times B[/tex]

[tex]\tau=NIABsin(90-57)[/tex]

[tex]\tau=520\times 3.9\ A\times \pi (0.007\ m)^2\times 0.982\ T\ cos(57)[/tex]

[tex]\tau=0.1669\ N-m[/tex]

[tex]\tau=0.167\ N-m[/tex]

So, the magnitude of torque is 0.1669 N-m. Hence, this is the required solution.

Answer:

t = 4.35 s

Explanation:

Since the balloon is moving upwards while the sand bag is dropped from it

so here the velocity of sand bag is same as the velocity of balloon

so here we can use kinematics to find the time it will take to reach the ground

[tex]\Delta y = v_y t + \frac{1}{2} gt^2[/tex]

here we know that since sand bag is dropped down so we have

[tex]\Delta y = -85.8 m[/tex]

initial upward speed is

[tex]v_y = 1.55 m/s[/tex]

also we know that gravity is downwards so we have

[tex]a = - 9.8 m/s^2[/tex]

so here we have

[tex]-85.8 = 1.55 t - \frac{1}{2}(9.8) t^2[/tex]

[tex]4.9 t^2 - 1.55 t - 85.8 = 0[/tex]

[tex]t = 4.35 s[/tex]

The distance traveled by a particle with velocity function

over the first t seconds can be obtained by integrating that function from 0 to t using integration by parts.

The distance traveled by a particle can essentially be obtained by integrating the velocity function over a given timeframe. In this case, the velocity function is given by

To calculate the distance traveled over the first t seconds, we need to integrate this function from 0 to t. Therefore, the integral ∫v(t)dt from 0 to t will provide the required solution. Use the method of integration by parts, choosing u=t^2 and

then complete the integration process following the standard procedure.

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Answer:

0.081 m /s

Explanation:

According to the conservation of momentum, the momentum of a system is conserved when no external force is applied on a body.

momentum of the system before throwing = momentum of the system after throwing

Let v be the velocity of quarterback after throwing the football.

80 x 0 + 0.43 x 0 = 80 x v + 0.43 x 15

0 = 80 v + 6.45

v = - 0.081 m /s

The negative sign shows that he is moving in backward direction.

The quarterback will be moving backward at approximately 0.080625 m/s just after releasing the football due to the conservation of momentum.

The student's question involves practicing Problem-Solving Strategy 11.1 for conservation of momentum problems. Specifically, the student is asked to calculate how fast an 80-kg quarterback will be moving backward just after releasing a football that has a mass of 0.43 kg and is thrown horizontally at a speed of 15 m/s. To solve this, we use the principle of conservation of momentum, which states that the total momentum of a system remains constant if no external forces act on it.

Before the throw, the total momentum of the system (quarterback and football) is zero because both are stationary with respect to horizontal motion. After the throw, the combined momentum must still be zero. We can set up the equation mQB × vQB + mball × vball = 0, where mQB is the mass of the quarterback, vQB is the quarterback's velocity after the throw, mball is the mass of the football, and vball is the velocity of the football. This simplifies to vQB = -(mball × vball) / mQB.

Plugging in the numbers gives us vQB = -(0.43 kg × 15 m/s) / 80 kg, which yields a velocity of vQB ≈ -0.080625 m/s. The negative sign indicates that the quarterback is moving in the opposite direction of the throw, which is backward.

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Answer:

Magnitude of the acceleration due to gravity on the planet = 2.34 m/s²

Explanation:

Time period of simple pendulum is given by

         [tex]T=2\pi\sqrt{\frac{l}{g}}[/tex], l is the length of pendulum, g is acceleration due to gravity value.

We can solve acceleration due to gravity as

            [tex]g=\frac{4\pi^2l}{T^2}[/tex]

Here

  Length of pendulum = 1.20 m

  Pendulum executes simple harmonic motion and makes 100 complete oscillations in 450 s.

  Period, [tex]T=\frac{450}{100}=4.5s[/tex]

Substituting

         [tex]g=\frac{4\pi^2\times 1.2}{4.5^2}=2.34m/s^2[/tex]

Magnitude of the acceleration due to gravity on the planet = 2.34 m/s²

Explanation:

Charge of electron in He, [tex]q_e=1.6\times 10^{-19}\ kg[/tex]

Charge of proton in He, [tex]q_p=1.6\times 10^{-19}\ kg[/tex]

Distance between them, [tex]d=2.7\times 10^{-10}\ m[/tex]

We need to find the electric force between them. It is given by :

[tex]F=k\dfrac{q_eq_p}{d^2}[/tex]

[tex]F=-9\times 10^9\times \dfrac{(1.6\times 10^{-19}\ C)^2}{(2.7\times 10^{-10}\ m)^2}[/tex]

[tex]F=-3.16\times 10^{-9}\ N[/tex]

Since, there are two protons so, the force become double i.e.

[tex]F=2\times 3.16\times 10^{-9}\ N[/tex]

[tex]F=6.32\times 10^{-9}\ N[/tex]

So, the correct option is (c). Hence, this is the required solution.

Answer:

9.66 x 10^-6 m

Explanation:

Use the Wein's displacement law

[tex]\lambda _{m}\times T = b[/tex]

Where, b is the Wein's constant

b =  2.898 x 10^-3 meter-kelvin

So, λm x 300 =  2.898 x 10^-3

λm = 9.66 x 10^-6 m

Explanation:

Given that,

Terminal voltage = 3.200 V

Internal resistance [tex]r= 5.00\ \Omega[/tex]

(a). We need to calculate the current

Using rule of loop

[tex]E-IR-Ir=0[/tex]

[tex]I=\dfrac{E}{R+r}[/tex]

Where, E = emf

R = resistance

r = internal resistance

Put the value into the formula

[tex]I=\dfrac{3.200}{1.00\times10^{3}+5.00}[/tex]

[tex]I=3.184\times10^{-3}\ A[/tex]

(b). We need to calculate the terminal voltage

Using formula of terminal voltage

[tex]V=E-Ir[/tex]

Where, V = terminal voltage

I = current

r = internal resistance

Put the value into the formula

[tex]V=3.200-3.184\times10^{-3}\times5.00[/tex]

[tex]V=3.18\ V[/tex]

(c). We need to calculate the ratio of the terminal voltage of voltmeter equal to emf

[tex]\dfrac{Terminal\ voltage}{emf}=\dfrac{3.18}{3.200 }[/tex]

[tex]\dfrac{Terminal\ voltage}{emf}= \dfrac{159}{160}[/tex]

Hence, This is the required solution.

The current flowing in the circuit is 3.195 milliamps. The terminal voltage is calculated to be 2.984V. The ratio of the terminal voltage to the emf is 0.9325 which shows that the terminal voltage is 93.25% of the emf due to the voltage drop resulted from the internal resistance of the battery.

The question is about the terminal voltage and internal resistance of a battery. To answer this, first we need to understand that terminal voltage is the potential difference (voltage) between two terminals of a battery, and it's slightly less than the emf due to internal resistance of the battery.

(a) The current (I) in the circuit is found using Ohm’s law: I = emf / (R_load + r) = 3.200V / (1.00kΩ + 5.00Ω) = 3.195 milliamps.

(b) The terminal voltage (V) is calculated by: V = emf - Ir = 3.200V - (3.195mA * 5.00Ω) = 2.984V.

(c) The ratio of the measured terminal voltage to the emf is V / emf = 2.984V / 3.200V = 0.9325. This shows that the terminal voltage is 93.25% of the emf, which accounts for the voltage drop due to the internal resistance of the battery.

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The wavelengths in the system's emission spectrum, in ascending order, are [tex]\(146 \, \text{nm}\) and \(249 \, \text{nm}\).[/tex]

To find the wavelengths associated with the allowed energies of the quantum system, we can use the formula for the energy of a photon:

[tex]\[ E = \frac{hc}{\lambda} \][/tex]

where:

-[tex]\( E \)[/tex] is the energy of the photon,

- [tex]\( h \)[/tex] is Planck's constant[tex](\( 6.626 \times 10^{-34} \, \text{J} \cdot \text{s} \)),[/tex]

- [tex]\( c \)[/tex] is the speed of light [tex](\( 3.00 \times 10^8 \, \text{m/s} \)),[/tex]

- [tex]\( \lambda \)[/tex] is the wavelength of the photon.

Given the energies [tex]\(0.0 \, \text{eV}\), \(5.0 \, \text{eV}\), and \(8.5 \, \text{eV}\)[/tex], we need to convert these energies to joules, since the units in the formula for energy are in joules.

1.[tex]\(0.0 \, \text{eV}\) corresponds to \(0.0 \, \text{J}\),[/tex]

2. [tex]\(5.0 \, \text{eV}\) corresponds to \(5.0 \times 1.602 \times 10^{-19} \, \text{J}\),[/tex]

3. [tex]\(8.5 \, \text{eV}\) corresponds to \(8.5 \times 1.602 \times 10^{-19} \, \text{J}\).[/tex]

Now, we can use these energies to calculate the wavelengths of the photons:

1. For [tex]\(0.0 \, \text{J}\):[/tex]

[tex]\[ \lambda = \frac{hc}{E} = \frac{(6.626 \times 10^{-34} \, \text{J} \cdot \text{s}) \times (3.00 \times 10^8 \, \text{m/s})}{0.0 \, \text{J}}} \][/tex]

2. For [tex]\(5.0 \times 1.602 \times 10^{-19} \, \text{J}\)[/tex]:

[tex]\[ \lambda = \frac{(6.626 \times 10^{-34} \, \text{J} \cdot \text{s}) \times (3.00 \times 10^8 \, \text{m/s})}{5.0 \times 1.602 \times 10^{-19} \, \text{J}} \]\[ \lambda \approx \frac{1.995 \times 10^{-25}}{5.0 \times 1.602} \, \text{m} \]\[ \lambda \approx 2.49 \times 10^{-8} \, \text{m} \][/tex]

3. For [tex]\(8.5 \times 1.602 \times 10^{-19} \, \text{J}\):[/tex]

[tex]\[ \lambda = \frac{(6.626 \times 10^{-34} \, \text{J} \cdot \text{s}) \times (3.00 \times 10^8 \, \text{m/s})}{8.5 \times 1.602 \times 10^{-19} \, \text{J}} \]\[ \lambda \approx \frac{1.995 \times 10^{-25}}{8.5 \times 1.602} \, \text{m} \]\[ \lambda \approx 1.46 \times 10^{-8} \, \text{m} \][/tex]

Now, let's convert these wavelengths to nanometers:

[tex]\( 2.49 \times 10^{-8} \, \text{m} = 249 \, \text{nm} \),[/tex]

[tex]. \( 1.46 \times 10^{-8} \, \text{m} = 146 \, \text{nm} \)[/tex]

So, the wavelengths in the system's emission spectrum, in ascending order, are [tex]\(146 \, \text{nm}\) and \(249 \, \text{nm}\).[/tex]

Answer:

Final angular speed equals 3 revolutions per second

Explanation:

We shall use conservation of angular momentum principle to solve this problem since the angular momentum of the system is conserved

[tex]L_{disk}=I_{disk}\omega \\\\L_{disk}=\frac{1}{2}mr^{2}\\\therefore L_{disk}=\frac{1}{2}mr^{2}\times10rad/sec[/tex]

After the disc and the dropped rod form a single assembly we have the final angular momentum of the system as follows

[tex]L_{final}=I_{disk+rod}\times \omega_{f} \\\\I_{disk+rod}=\frac{1}{2}mr_{disc}^{2}+\frac{1}{12}mL_{rod}^{2}\\I_{disk+rod}=\frac{1}{2}mr_{disc}^{2}+\frac{1}{12}m\times (2r_{disc})^{2}\\\\I_{disk+rod}=\frac{1}{2}mr_{disc}^{2}+\frac{1}{3}mr_{disc}^{2}\\\\L_{final}=\frac{5mr_{disc}^{2}}{6}\times \omega _{f}\\\\[/tex]

Equating initial and final angular momentum we have

[tex]\frac{5mr_{disc}^{2}}{6}\times \omega _{f}=\frac{1}{2}m_{disc}\times r_{disc}^{2}\times 10\pi rad/sec[/tex]

Solving for [tex]\omega_{f}[/tex] we get

[tex]\omega_{f}=6\pi rad/sec[/tex]

Thus no of revolutions in 1 second are 6π/2π

No of revolutions are 3 revolutions per second

Answer:

change that a lead is 0.13533

Explanation:

µ  = 50000

f(t) = [e^(-t/µ )]/[µ      if  t ≥ 0

f(t) = 0  if  t < 0

τ = 100000

to find out

the chance that a led will last

solution

we know function is f(t) = [e^(-τ/µ)]/[µ]    

τ = 100000

so we can say that probability (τ  ≥ 100000 ) that is

= 1 - Probability ( τ ≤ 100000 )

that is function of F so

= 1 - f ( 100000 )

that will be

= 1 - ( 1 - [e^(-τ/µ)]/[µ]   )

put all value here τ = 100000 and µ = 50000

= 1 - ( 1 - [e^(-100000/50000)]  )

= 1 - 1 - [e^(-100000/50000)]

= 0.13533

so that change that a lead is 0.13533

Answer:

decrease

Explanation:

If the two charged ball attracts each other, it means the charge on both the balls are opposite in nature.

As, we insert a glass slab, it means a dielectric is inserted in between the charges. The force between them is reduced.

Answer:

a) 1.34 Volts

b) 3.08 W

c) 2.68 W

Explanation:

Given:

Emf of the cell, E = 1.54 V

current, i = 2.0 A

internal resistance, r = 0.100Ω

(a) Terminal voltage (V) = E - v

where,

v is the potential difference across the resistance 'r'

now,

according to the Ohm's Law, we have

v = i × r  

substituting the values in the above equation we get

v = 2.0 × 0.100 = 0.2 Volts

thus,

Terminal voltage (V) = (1.54 - 0.2) = 1.34 V

(b) Now, the Total power (P) is given as

P = E × i = (1.54 × 2.0) = 3.08 W  

(c) Power into its load = [terminal voltage, v] * i  

= (1.34 × 2.0) = 2.68 W

Final answer:

Terminal voltage of a carbon-zinc cell is 1.34 V, producing 2.68 W of electrical power, with 2.68 W going to the load.

Explanation:

Terminal voltage: The formula to calculate terminal voltage is V = EMF - I * r, where V is the terminal voltage, EMF is the electromotive force, I is the current, and r is the internal resistance of the cell. So, V = 1.54 V - 2.00 A * 0.100 Ω = 1.34 V.

Electrical power: The electrical power produced by the cell is given by P = V * I, where P is power, V is voltage, and I is current. Substituting the values, P = 1.34 V * 2.00 A = 2.68 W.

Power to load: The power delivered to the load is equal to the voltage supplied to the load times the current flowing through it. Hence, the power to the load is P = V_load * I = 1.34 V * 2.00 A = 2.68 W.

Answer:

133280 N

Explanation:

Volume, V = 1 m^3

density of mercury, d = 13.6 x 10^3 kg/m^3

Buoyant force, F = Volume immersed x density of mercury x g

F = 1 x 13.6 x 1000 x 9.8

F = 133280 N

Answer:

The height is 1,225 meters

Explanation:

DistanceX= speedX × time ⇒ time= (5 meters) ÷ (10 meters/second) = 0,5 seconds

DistanceY= high= (1/2) × g × (time^2) = (1/2) × 9,8 (meters/(second^2)) × 0,25 (second^2) = 1,225 meters

im not that smart but maybe 2 x the mass of the wieght will give u the answer

Answer:

Explanation:

A proton is positively charged in nature.

Let an electric field strength is E.

The force on a charged particle placed in an electric field is given by

F = q x E

Where q is the charge

Here, the proton is positively charged, so the direction of force acting on the proton is same as teh direction of electric field strength.

Thus, the motion of proton is parallel to the electric field and the motion is accelerated.