A vertical block-spring system on earth has a period of 6.0 s. What is the period of this same system on the moon where the acceleration due to gravity is roughly 1/6 that of earth? A)1.0s B)2.4s C)6.0s D)15s E)36s

Answer:

Option B is the correct answer.

Explanation:

Thermal expansion

            [tex]\Delta L=L\alpha \Delta T[/tex]

L = 1.2 meter

ΔT = 65 - 15 = 50°C

Thermal Expansion Coefficient for aluminum, α = 24 x 10⁻⁶/°C

We have change in length

          [tex]\Delta L=L\alpha \Delta T=1.2\times 24\times 10^{-6}\times 50=1.44\times 10^{-3}m[/tex]

New length = 1.2 + 1.44 x 10⁻³ = 1.2014 m

Option B is the correct answer.

Answer:

B. 1.201386 meters

Explanation:

The length of an aluminum rod at 65°C if its length at 15°C is 1.2 meters is 1.201386 meters.

Answer:

8000

Explanation:

V²=U²+2as

V=400m/s

U=0

a=10

s=?

(400)²=(0)²+2*10*a

160,000=20s

s=160,000/20

s=8000

Answer:

[tex]\Delta \rho =0.18/mL326gm[/tex]

Explanation:

we have error in division of 2 quantities is related as

[tex]z=\frac{a}{b}\\\\\frac{\Delta z}{z}=\frac{\Delta a}{a}+\frac{\Delta b}{b}[/tex]

where [tex]\Delta a,\Delta b[/tex] are errors in quantities a,b

Thus error in density becomes

[tex]\Delta \rho =\rho _{0}\times(\frac{\Delta m}{m}+\frac{\Delta V}{V})[/tex]

Applying values we get

[tex]\Delta \rho =\frac{4.635}{1.13} \times(\frac{0.002}{4.635}+\frac{0.05}{1.13})[/tex]

thus [tex]\Delta \rho =0.18326gm/mL[/tex]

Answer:

4.5 x 10¹⁴ Hz

666.7 nm

1.8 x 10⁵ J

The color of the emitted light is red

Explanation:

E = energy of photons of light = 2.961 x 10⁻¹⁹ J

f = frequency of the photon

Energy of photons is given as

E = h f

2.961 x 10⁻¹⁹ = (6.63 x 10⁻³⁴) f

f = 4.5 x 10¹⁴ Hz

c = speed of light = 3 x 10⁸ m/s

λ = wavelength of photon

Using the equation

c = f λ

3 x 10⁸ = (4.5 x 10¹⁴) λ

λ = 0.6667 x 10⁻⁶ m

λ = 666.7 x 10⁻⁹ m

λ = 666.7 nm

n = number of photons in 1 mole = 6.023 x 10²³

U = energy of 1 mole of photons

Energy of 1 mole of photons is given as

U = n E

U = (6.023 x 10²³) (2.961 x 10⁻¹⁹)

U = 1.8 x 10⁵ J

The color of the emitted light is red

The frequency and wavelength of a photon with energy of 2.961 × 10-19 J are approximately 4.468 x 10¹4 s¯¹ and 656.3 nm, respectively. The energy of one mole of these photons is approximately 1.823 x 10⁵ J mol-¹. The color of the light emitted by these photons is red.

The energy of a photon of light can be calculated into both a frequency and wavelength using the Planck-Einstein relation E = hf, and the speed of light relation c = λf, where h is Planck's constant, c is the speed of light, and λ is wavelength.

Let's first find the frequency. Given that the energy E is 2.961 × 10-19 J and the value of Planck's constant h is 6.63 × 10-³4 J·s (approximately), you can solve for the frequency f = E/h, which results in approximately 4.468 × 10¹4 s¯¹.

To find the wavelength, you can use the light speed equation c = fλ. Given the speed of light c is approximately 3.00 × 10⁸ m/s and using the frequency calculated above, solve for λ = c/f, which results in approximately 656.3 nm.

To find the energy of one mole of these photons, use Avogadro's number (6.022 x 10²³ photons/mole) and the provided energy of a single photon. The total energy is then calculated as E = (2.961 × 10-19 J/photon) x (6.022 x 10²³ /mole) = 1.823 × 10⁵ J mol-¹.

Lastly, the color of the photon can be inferred from its wavelength. As the wavelength is 656.3 nm, this falls within the range of the visible light spectrum for the color red.

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Answer:

0.51 m

Explanation:

Given :

Plank length = 2.65 m

Distance from the ledge from which the cable is attached = 79.7 cm = 0.797 m

Angle = 40.3 degree

Mass of the man, m = 76.4 kg

Now the net torque acting on the plank is zero.

Therefore, maximum torque applied by cable is

    = 2648 x 0.797 x cos (40.3)

    = 1609.5 N-m

We know that the man should apply the same torque,

Therefore, x [tex]\times[/tex]76.4 [tex]\times[/tex] g = 1609.5

                  x =2.14 m

Therefore, length to the end of the plank is = 2.65-2.14

                                                                         =0.51 m

Answer:

8.83 rad/s²

Explanation:

w₀ = initial angular speed of the disk = 0 rad/s

w = final angular speed of the disk = 30.3 rad/s

t = time period of rotation of the disk = 3.43 sec

[tex]\alpha[/tex] = Angular acceleration of the disk

Angular acceleration of the disk is given as

[tex]\alpha = \frac{w-w_{o}}{t}[/tex]

inserting the values

[tex]\alpha[/tex] = (30.3 - 0)/3.43

[tex]\alpha[/tex] = 8.83 rad/s²

Answer:

t = 141.55 years

Explanation:

As we know that the radius of the wire is

r = 2.00 cm

so crossectional area of the wire is given as

[tex]A = \pi r^2[/tex]

[tex]A = \pi(0.02)^2[/tex]

[tex]A = 1.26 \times 10^{-3} m^2[/tex]

now we know the free charge density of wire as

[tex]n = 8.50 \times 10^{28}[/tex]

so drift speed of the charge in wire is given as

[tex]v_d = \frac{i}{neA}[/tex]

[tex]v_d = \frac{1190}{(8.50 \times 10^{28})(1.6 \times 10^{-19})(1.26\times 10^{-3})}[/tex]

[tex]v_d = 6.96 \times 10^{-5} m/s[/tex]

now the time taken to cover whole length of wire is given as

[tex]t = \frac{L}{v_d}[/tex]

[tex]t = \frac{310 \times 10^3}{6.96 \times 10^{-5}}[/tex]

[tex]t = 4.46 \times 10^9 s[/tex]

[tex]t = 141.55 years[/tex]

Answer:

Radius = 7.75 mm

Explanation:

magnetic field inside a point in the wire is given as

[tex]B = \frac{\mu_0 i r}{2\pi R^2}[/tex]

now we have

[tex]3mT = \frac{\mu_0 i (6mm)}{2\pi R^2}[/tex]

now outside wire magnetic field is given as

[tex]B = \frac{\mu_0 i}{2\pi r}[/tex]

now we have

[tex]1.50 mT = \frac{\mu_0 i}{2\pi(20 mm)}[/tex]

now divide above two equations

[tex]2 = \frac{6 mm\times 20 mm}{R^2}[/tex]

[tex]R = 7.75 mm[/tex]

Answer:

37.725 A

Explanation:

B = magnitude of the magnetic field produced by the electric wire = 0.503 x 10⁻⁴ T

r = distance from the wire where the magnetic field is noted = 15 cm = 0.15 m

i = magnitude of current flowing through the wire = ?

Magnetic field by a long wire is given as

[tex]B = \frac{\mu _{o}}{4\pi }\frac{2i}{r}[/tex]

Inserting the values

[tex]0.503\times 10^{-4} = (10^{-7})\frac{2i}{0.15}[/tex]

i = 37.725 A

The final temperature of the system consisting of the ice, water, and calorimeter is approximately 6.8°C.

Here's how you can calculate it step by step:

1. Calculate the heat absorbed by the ice to reach 0°C:

[tex]\[ Q_1 = mc\Delta T \]\[ Q_1 = 40 g \times 2090 J/kg^\circ C \times (0^\circ C - (-69^\circ C)) \]\[ Q_1 = 40 g \times 2090 J/kg^\circ C \times 69^\circC \]\[ Q_1 = 571560 J \][/tex]

2. Calculate the heat absorbed by the ice to melt completely:

[tex]\[ Q_2 = mL_f \]\[ Q_2 = 40 g \times 334 J/g \]\[ Q_2 = 13360 J \][/tex]

3. Calculate the heat absorbed by the melted ice to reach the final temperature (assuming the final temperature is T):

[tex]\[ Q_3 = mc\Delta T \]\[ Q_3 = 40 g \times 4186 J/kg°C \times (T - 0°C) \]\[ Q_3 = 167440T J \][/tex]

4. Calculate the heat absorbed by the water and calorimeter to reach the final temperature (T):

[tex]\[ Q_4 = mc\Delta T \]\[ Q_4 = (590 g + 80 g) \times 4186 J/kg°C \times (T - 22°C) \]\[ Q_4 = 270104T - 114208 \][/tex]

Now, since heat gained = heat lost (assuming no heat loss to the surroundings):

[tex]\[ Q_1 + Q_2 + Q_3 = Q_4 \]\[ 571560 + 13360 + 167440T = 270104T - 114208 \]\[ 571560 + 13360 + 114208 = 270104T - 167440T \]\[ 699128 = 102664T \]\[ T \aprrox 6.8°C \][/tex]

The final temperature of the system is approximately 6.8°C.

Complete Question:
A 40 g block of ice is cooled to -69°C and is then added to 590 g of water in an 80 g copper calorimeter at a temperature of 22°C. Determine the final temperature of the system consisting of the ice, water, and calorimeter. Remember that the ice must first warm to 0°C, melt, and then continue warming as water. The specific heat of ice is 0.500 cal/g·°C = 2090 J/kg°C.

Answer:

(ii) The Electric Field reports the Electric Force on a 1C test charge placed at a particular location.

(iii) The Electric Potential reports the Electric Potential energy of a 1C test charge place at a particular location.

(iv) The spatial derivative of the electric potential at a particular location reports the electric field at that location.

ii, iii and iv are true.

Explanation:

Electric force per unit charge  is the electric field. It is a vector. E = F/q.

Electric potential is the electric potential energy per unit charge and is a scalar quantity, like the electric potential. V = U/q where U is the electric potential energy and q the charge.

Electric field exists due to a difference of potential, between two different points.E =dV/dx .

Option (ii),(iii) & (iv) is correct.

The question posed deals with the concepts of Electric Force, Electric Field, Electric Potential, and Electric Potential Energy in the context of physics. Let's analyze each statement:

Electric Force, Electric Field, and Electric Potential are vectors; Electric Potential Energy is a scalar value. This statement is partially incorrect. Electric Force and Electric Field are indeed vectors because they have both magnitude and direction. However, Electric Potential is a scalar quantity, not a vector, because it only has magnitude without direction. Electric Potential Energy is correctly identified as a scalar value.

The Electric Field reports the Electric Force on a 1C test charge placed at a particular location. This statement is true. The Electric Field is defined as the Electric Force per unit charge, and it indeed represents the force that a 1 coulomb test charge would experience at that point.

The Electric Potential reports the Electric Potential energy of a 1C test charge placed at a particular location. This statement is true. Electric Potential is the amount of Electric Potential Energy per unit charge that a test charge would have in a particular location in the electric field.

The spatial derivative of the electric potential at a particular location reports the electric field at that location. This statement is true. According to electrostatics, the electric field at a point is the negative gradient (spatial derivative) of the electric potential at that point.

It is essential to understand that electric potential is different from an electric field: the former is a scalar that represents potential energy per unit charge, while the latter is a vector representing the force per unit charge. Calculating the scalar electric potential is generally simpler than calculating the vector electric field.

Answer:

d. 5.7 x 10⁴ J

Explanation:

I = moment of inertia of the flywheel = 0.525 kg-m²

w₀ = initial angular speed of the flywheel = 69.1 rad/s

w = final angular speed of the flywheel = 471 rad/s

W = work done by the engine on the flywheel

Work done by the engine is given as

W = (0.5) I (w² - w₀²)

Inserting the values

W = (0.5) (0.525) (471² - 69.1²)

W = 5.7 x 10⁴ J

Answer:

Rate = k[aryl halide][nucleophile]

Explanation:

The simple aryl halides are almost inert to usual nucleophilic reagents but considerable activation on the ring can be produced by the addition of strongly electron-attracting substituents on either the ortho or para positions, or both. These groups deactivate the ring to allow the attack of the nucleophille on the ring.

Thus, these reactions can occur by following addition-elimination mechanism in which the nucleophille first attacks the aryl halide and then the elimination of the leaving group takes place.

Kinetic studies of this type of mechanism demonstrate that the reactions are of second-order kinetics– first order w.r.t. nucleophile and also, first-order w.r.t. aromatic substrate. The rate determining step (r.d.s.) is the formation of the addition intermediate.

Thus,

Rate = k[aryl halide][nucleophile]

Answer:

13.79 revolutions

Explanation:

Velocity of ball = v = 34.5 m/s

Spin rate of ball = 26 revolutions/s

Distance between home plate and pitching mound = s = 18.3 m

Time taken by the ball to reach the home plate = t

[tex]t=\frac{18.3}{34.5}\ s[/tex]

Number of revolutions the ball completes is

[tex]26\times \frac{18.3}{34.5}=13.79[/tex]

∴Number of revolutions the ball completes before reaching home plate is 13.79

Answer:

The number of revolutions is 13.78

Explanation:

Given data:

v = speed = 34.5 m/s

d = distance = 18.3 m

spin rate = 26 rev/s

The time taken is equal to:

[tex]t=\frac{d}{v} =\frac{18.3}{34.5} =0.53s[/tex]

The number of revolutions is equal:

N = 0.53 * 26 = 13.78 rev

Answer:

541.89 Watt

Explanation:

Consider the motion of rock on rough surface

μ = Coefficient of kinetic friction = 0.63

acceleration caused to kinetic friction is given as

a = - μg

a = - (0.63) (9.8)

a = - 6.2 m/s²

v₀ = initial velocity of the rock = 9.25 m/s

t = time taken to stop

v = final velocity = 0 m/s

Using the equation

v = v₀ + a t

0 = 9.25 + (- 6.2) t

t = 1.5 sec

m = mass of the rock = 19 kg

Energy lost due to friction is given as

E = (0.5) m (v₀² - v²)

E = (0.5) (19) (9.25² - 0²)

E = 812.84 J

Average thermal power is given as

[tex]P = \frac{E}{t}[/tex]

[tex]P = \frac{812.84}{1.5}[/tex]

P = 541.89 Watt

Answer:

From ohms law,

V=IR

R=V/I =12.0/150 =0.08 ohm.

Answer:

The velocity at discharge is 100.46 ft/s

Explanation:

Given that,

Pressure = 68 psi

We need to calculate the pressure in pascal

[tex]P=68\times6894.74\ Pa[/tex]

[tex]P=468842.32\ Pa[/tex]

We need to calculate the velocity

Let the velocity is v.

Using Bernoulli equation

[tex]P=\dfrac{1}{2}\rho v^2[/tex]

[tex]468842.32=0.5\times1000\times v^2[/tex]

[tex]v=\sqrt{\dfrac{468842.32}{0.5\times1000}}[/tex]

[tex]v=30.62\ m/s[/tex]

Now, We will convert m/s to ft/s

[tex]v =30.62\times3.281[/tex]

[tex]v=100.46\ ft/s[/tex]

Hence, The velocity at discharge is 100.46 ft/s

The speed of water discharged from a hose depends on the nozzle pressure and the constriction of the flow, but the specific speed cannot be determined from pressure alone without additional parameters.

The question is asking about the velocity or speed achieved by water when it is forced out of a hose with a nozzle pressure of 68 psi. To understand this, we need to know that the pressure within the hose is directly correlated with the speed of the water's exit. This is due to the constriction of the water flow by the nozzle, causing speed to increase.

However, the specific velocity at discharge can't be straightforwardly calculated from pressure alone without knowing more details, such as the dimensions of the hose and nozzle, and the properties of the fluid. Therefore, based on the provided information, a specific answer in ft/sec can't be given.

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Answer:

option C

multiplication factor n = 1 when volume change to half and pressure become double

Explanation:

we know by Ideal Gas law:

P1V1 = nRT1

P2V2 = nRT2

according to the question

pressure is doubled and volume is reduced to half  

so we have

new pressure = 2*P1

new volume = V1/2

hence,

(2P1) * (V1/2) = nRT2

P1V1 = nRT2

we have now

nRT1 = nRT2

we get

T1 = T2

thus no change in temperature

we know that internal energy is given as

internal energy = nCvT,

since temperature is directly proportional to internal energy and since temperature remains constant therefore internal energy remains constant

So there is no change in internal energy

thus, multiplication factor n = 1 when volume change to half and pressure change to double

Answer:

option (a)

Explanation:

The direction of magnetic field is given by Fleming's left hand rule.

If we spread the fore finger, middle finger and the thumb of our right hand such that they are mutually perpendicular to each other, then the direction of force is in the direction of thumb, direction of magnetic field is given by the direction of fore finger and the middle finger indicates the direction of current .

Here, current is upwards, magnetic force is rightwards, so the direction of magnetic field is given in outwards from the screen.

Answer:

[tex]v_f = 27.9 m/s[/tex]

Explanation:

Component of the weight of the truck along the inclined plane is given as

[tex]F_1 = W sin\theta[/tex]

[tex]F_1 = 15000 sin15[/tex]

[tex]F_1 = 3882.3 N[/tex]

also the engine is providing the constant force to it as

[tex]F_2 = 8000 N[/tex]

now the net force along the the plane is given as

[tex]F_{net} = 8000 + 3882.3[/tex]

[tex]F = 11882.3 N[/tex]

mass of the truck is given as

[tex]m = \frac{w}{g} = 1529 kg[/tex]

now the acceleration is given as

[tex]a = \frac{F}{m}[/tex]

[tex]a = 7.77 m/s^2[/tex]

now the speed of the truck after travelling distance of d = 50 m is given as

[tex]v_f^2 = v_i^2 + 2 a d[/tex]

[tex]v_f^2 = 0 + 2(7.77)(50)[/tex]

[tex]v_f = 27.9 m/s[/tex]

To calculate the minimum uncertainty in the speed of the molecule, we can use the Heisenberg uncertainty principle. The uncertainty in position is equal to the molecular diameter, and the uncertainty in momentum can be calculated using the uncertainty principle equation. Finally, the uncertainty in velocity can be found by dividing the uncertainty in momentum by the mass of the molecule.

To calculate the minimum uncertainty in the speed of the molecule, we can use the Heisenberg uncertainty principle. The uncertainty in position (Ax) is equal to the molecular diameter, which is given as 0.70 nm. The uncertainty in momentum (Ap) can be calculated using the equation AxAp ≥ h/4. Once the uncertainty in momentum is found, the uncertainty in velocity can be found from Ap = mΔv, where m is the mass of the molecule.

Using the given values, the uncertainty in position (Ax) is 0.70 nm. Plugging this into the uncertainty principle equation and solving for Ap, we get Ap ≥ h/4Ax. Substituting the values for h and Ax, we have Ap ≥ (6.626 × 10-34 J·s)/(4 × 0.70 × 10-9 m).

Next, we can find the uncertainty in velocity (Δv) by using Ap = mΔv. Rearranging the equation, we have Δv = Ap/m. Plugging in the values for Ap (obtained from the previous calculation) and the mass of the molecule, we can calculate the minimum uncertainty in the speed of the molecule.

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Answer:

5400 W-hr

Explanation:

Given:

Power used by energy efficient bulb = 15 W

Power used by incandescent bulb = 60 W

Total time of bulb used = 4 hours/day × 30 days = 120 hours

Now,

Energy used by the individual bulb by using them for 120 hours

we know,

Energy = Power × Time

thus,

Energy consumed by energy efficient bulb = 15 W × 120 hour = 1800 W-hr

Energy consumed by  incandescent bulb = 60 W × 120 hour = 7200 W-hr

hence,  the energy saved will be = 7200 - 1800 = 5400 W-hr

Final answer:

Calculating the monthly energy savings involves finding the difference in power consumption between a 60 W incandescent bulb and a 15 W energy efficient bulb, multiplying by the daily usage, and the number of days in a month. The savings are 45 W per hour, equating to 180 Wh/day and 5.4 kWh/month.

Explanation:

The question asks how much energy is saved each month by using an energy efficient light bulb instead of an incandescent light bulb for 4 hours a day. To calculate the energy saved, we need to determine the difference in power consumption between the two types of bulbs, multiply that difference by the number of hours used per day, and then by the number of days in a month.

Firstly, we find the power saved per hour:

60 W (incandescent) - 15 W (efficient) = 45 W saved per hour

Next, we calculate the daily savings:

45 W x 4 hours/day = 180 Wh/day

Finally, we calculate the monthly savings:

180 Wh/day x 30 days/month = 5400 Wh/month

Since 1 kWh = 1000 Wh, the saving is 5.4 kWh/month

This is the amount of energy saved by using the energy efficient bulb instead of the incandescent bulb for 4 hours each day over a month.

Answer:

2.05 x 10^8 m /s

Explanation:

c = 3 x 10^8 m/s

μ = c / v

where, μ is the refractive index, c be the velocity of light in air and v be the velocity of light in the medium.

μ = 1.461

1.461 = 3 x 10^8 / v

v = 3 x 10^8 / 1.461

v = 2.05 x 10^8 m /s

Answer:

[tex]Area = 0.126 m^2[/tex]

Explanation:

Since the crossection of cylinder is of circular shape

so here the crossectional area will be given as

[tex]A = \pi r^2[/tex]

here we know that radius of the cylinder will be

[tex]R = 20 cm[/tex]

so in SI units it is given as

[tex]R = 0.20 m[/tex]

now we have

[tex]Area = \pi (0.20)^2[/tex]

[tex]Area = 0.126 m^2[/tex]

Answer:

The ladder is moving at the rate of 0.65 ft/s

Explanation:

A 16​-foot ladder is leaning against a building. If the bottom of the ladder is sliding along the pavement directly away from the building at 2 ​feet/second. We need to find the rate at which the top of the ladder moving down when the foot of the ladder is 5 feet from the​ wall.

The attached figure shows whole description such that,

[tex]x^2+y^2=256[/tex].........(1)

[tex]\dfrac{dx}{dt}=2\ ft/s[/tex]

We need to find, [tex]\dfrac{dy}{dt}[/tex] at x = 5 ft

Differentiating equation (1) wrt t as :

[tex]2x.\dfrac{dx}{dt}+2y.\dfrac{dy}{dt}=0[/tex]

[tex]2x+y\dfrac{dy}{dt}=0[/tex]

[tex]\dfrac{dy}{dt}=-\dfrac{2x}{y}[/tex]

Since, [tex]y=\sqrt{256-x^2}[/tex]

[tex]\dfrac{dy}{dt}=-\dfrac{2x}{\sqrt{256-x^2}}[/tex]

At x = 5 ft,

[tex]\dfrac{dy}{dt}=-\dfrac{2\times 5}{\sqrt{256-5^2}}[/tex]

[tex]\dfrac{dy}{dt}=0.65[/tex]

So, the ladder is moving down at the rate of 0.65 ft/s. Hence, this is the required solution.

This is a calculation of a related rates problem in calculus, using the Pythagorean Theorem. The calculation finds the rate of descent (db/dt) for the top of a ladder sliding down a wall. The final answer found is -1.5 feet/second, meaning the top of the ladder is moving downward at a rate of 1.5 feet per second when the ladder is 5 feet away from the building.

The question involves a concept in calculus known as related rates problem. It's a practical extension of the Pythagorean theorem where the sides of the right triangle formed by the ladder, building, and the ground are changing over time. In this case, a 16-feet ladder is sliding down a wall and we are to find the rate at which the top of the ladder is moving down when the foot of the ladder is 5 feet from the wall. First, we label the bottom (horizontal) side of our triangle 'a', the side along the wall (vertical) 'b', and the hypotenuse (ladder) 'c'. The Pythagorean theorem gives us a² + b² = c². Differentiating both sides with respect to time (t) gives us 2a(da/dt) + 2b(db/dt) = 2c(dc/dt). Here, we know that da/dt = 2 feet/sec (rate at which the ladder is moving away from the wall), c = 16 feet (length of the ladder), and a (distance from the wall) = 5 feet. Also, the ladder's length is not changing, so dc/dt = 0. Substituting these values, we can solve for db/dt (rate of descent of the ladder). The resultant rate of descent of the top of the ladder is -1.5 feet/second.

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Answer:

55.6 nC

Explanation:

The electric field at the surface of a charged sphere has the same expression of the electric field produced by a single point charge located at the centre of the sphere and having the same charge of the sphere, so it is given by

[tex]E=k\frac{Q}{r^2}[/tex]

where

[tex]k=9\cdot 10^9 N m^2 C^{-2}[/tex] is the Coulomb's constant

Q is the charge on the sphere

r is the radius of the sphere

In this problem we know

E = 890 N/C is the magnitude of the electric field on the sphere

r = 0.750 m is the radius of the sphere

So by re-arranging the equation we can find the net charge on the sphere:

[tex]Q=\frac{Er^2}{k}=\frac{(890)(0.750)^2}{9\cdot 10^9}=5.56\cdot 10^{-8} C=55.6 nC[/tex]

To find the net charge within the surface of the sphere, we can use Gauss's Law. The net electric flux through a closed surface enclosing a charge is equal to the charge divided by the electric constant, ε₀. Given the electric field and the radius of the sphere, we can calculate the net charge using the equation derived from Gauss's Law.

The electric field everywhere on the surface of a thin, spherical shell is radially inward and has a magnitude of 890 N/C. To find the net charge within the surface of the sphere, we can use Gauss's Law. The net electric flux through a closed surface enclosing a charge is equal to the charge divided by the electric constant, ε₀. In this case, the closed surface is the spherical shell and the electric field is constant on the surface, so the net electric flux is equal to the electric field multiplied by the surface area of the sphere. The surface area of the sphere is given by 4πr², where r is the radius of the sphere. Setting the net electric flux equal to the charge divided by ε₀, we can solve for the charge.

Given that the electric field is 890 N/C, the radius of the sphere is 0.750 m, and the electric constant, ε₀, is 8.99 x 10⁹ Nm²/C², we can plug in these values to solve for the charge.

Let Q be the net charge within the sphere's surface:

Net electric flux = Electric field * Surface area

Q / ε₀ = Electric field * Surface area

Q / (8.99 x 10⁹ Nm²/C²) = (890 N/C) * (4π(0.750 m)²)

Q = (890 N/C) * (4π(0.750 m)²) * (8.99 x 10⁹ Nm²/C²)

Solving this equation will give us the net charge within the sphere's surface.

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Answer:

a). The potential is highest at the center of the sphere

Explanation:

We k ow the potential of a non conducting charged sphre of radius R at a point r < R is given by

[tex]E=\left [ \frac{K.Q}{2R} \right ]\left [ 3-(\frac{r}{R})^{2} \right ][/tex]

Therefore at the center of the sphere where r = 0

[tex]E=\left [ \frac{K.Q}{2R} \right ]\left [ 3-0 \right ][/tex]

[tex]E=\left [ \frac{3K.Q}{2R} \right ][/tex]

Now at the surface of the sphere where r = R

[tex]E=\left [ \frac{K.Q}{2R} \right ]\left ( 3-1 \right )[/tex]

[tex]E=\left [ \frac{2K.Q}{2R} \right ][/tex]

[tex]E=\left [ \frac{K.Q}{R} \right ][/tex]

Now outside the sphere where r > R, the potential is

[tex]E=\left [ \frac{K.Q}{r} \right ][/tex]

This gives the same result as the previous one.

As [tex]r\rightarrow \infty , E\rightarrow 0[/tex]

Thus, the potential of the sphere is highest at the center.

The object is moving along a circular path. Given the time restriction, it completes a half revolution, which equates to half the circumference of the circle. Therefore, the object travels approximately 31.4 units.

The object is moving on a circular trajectory defined by r(t) = <10 cos 6t, 10 sin 6t>. This equation describes a circular path with a radius of 10 units. To find out how far the object travels, we can use the formula for the circumference of a circle, which is 2πr. However, since the time t varies from 0 to π, the object only makes a half revolution along the circle. So, the total distance the object travels would be equal to half the circumference of the circle, which is πr.

Substituting r = 10, we get, distance traveled = π*10 = 31.4 units approx.

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Answer:

Tangential speed, v = 314.15 m/s

Explanation:

It is given that,

Mass of the object, m = 15 kg

It is moving in a circle of radius, r = 10 m

Time period, t = 0.2 seconds

We need to find the tangential velocity of the object. It is given by :

[tex]v=\dfrac{2\pi r}{t}[/tex]

Where

v = tangential speed

[tex]v=\dfrac{2\pi \times 10\ m}{0.2\ s}[/tex]

v = 314.15 m/s

So, the tangential speed of the object is 314.15 m/s. Hence, this is the required solution.

Answer:

Part a)

[tex]q_2 = -6.8 \mu C[/tex]

Part b)

[tex]F = 0.700 N[/tex]

direction = downwards

Explanation:

As we know that the negative charge will experience the force due to some other charge below it

the force is given as

[tex]F = 0.700 N[/tex]

now we know that

[tex]F = \frac{kq_1q_2}{r^2}[/tex]

now plug in all data

[tex]0.700 = \frac{(9 \times 10^9)(0.550\mu C)q_2}{0.220^2}[/tex]

[tex]0.700 = 1.022\times 10^5 q_2[/tex]

[tex]q_2 = -6.8 \mu C[/tex]

since this is a repulsion force so it must be a negative charge

Part b)

As per Newton's III law it will exert equal and opposite force on it

So here the force on the charge below it will be same in magnitude but opposite in direction

so here we have

[tex]F = 0.700 N[/tex]

direction = downwards