6. The radius of a ball is (5.2 + 0.2) cm. The percentage
error in the volume of the ball is;​

Answer:

6.02 dB increase  

Explanation:

Let us take the initial power from the speaker P' = P Watt

then, the final power P = 4P Watt

for a given unit area, initial intensity (power per unit area) will be

I' = P Watt/m^2

and the final quadrupled sound will produce a sound intensity of

I = 4P Watt/m^2

Increase in loudness is gotten from the relation

ΔL =  [tex]10log_{10} \frac{I}{I'}[/tex]

where

I = final sound intensity

I' = initial sound intensity

imputing values of the intensity into the equation, we have

==>  [tex]10log_{10} \frac{4P}{P}[/tex] =  [tex]10log_{10} 4[/tex] = 6.02 dB increase  

Answer:

0.912

Explanation:

Given that

Height of bouncing of the ball, h = 1.71 m

Number of times the ball bounced, n = 4 times

Height from which the ball was dropped, H = 2.47

First, let's start by defining what coefficient of restitution means

Coefficient of Restitution, CoR is the "ratio of the final to initial relative velocity between two objects after they collide. It normally ranges from 0 to 1 where 1 would be a perfectly elastic collision."

It is mathematically represented as

CoR = (velocity after collision) / (velocity before collision)

1.71 = 2.47 * c^4, where c = CoR

1.71/2.47 = c^4

c^4 = 0.6923

c = 4th root of 0.6923

c = 0.912

Answer:

Explanation:

If a be grating element

a = 1 x 10⁻² / 11000

= .0909 x 10⁻⁵

= 909 x 10⁻⁹ m

for first order maxima , the condition is

a sinθ = λ where λ is wavelength

909 x 10⁻⁹ sin 49.67 = λ₁

λ₁ = 692.95  nm .

λ₂ = 909 x 10⁻⁹ sin 50.65

= 702.91 nm

λ₃ = 909 x 10⁻⁹ sin 52.06

= 716.88 nm

λ₄ = 909 x 10⁻⁹ sin 52.89

= 724.90 nm

692.95  nm ,  702.91 nm  , 716.88 nm , 724.90 nm .

Answer:

Explanation:

Force on charge particles

F = q ( v x B )

= 1.6 x 10⁻¹⁹ x [ ( 2i+3j+4k) x .5k ] x 10⁵

=  1.6 x 10⁻¹⁴ x  (  1.5 i - j )

= (2.4 i - 1.6 j ) x 10⁻¹⁴ N

magnitude of this vector

= 2.88 x 10⁻¹⁴ N

Angle between B and v

cosθ = [tex]\frac{(2i+3j+4k).(.5k)}{\sqrt{2^2+3^2+4^2}\times .5 }[/tex]

= [tex]\frac{2}{2.69}[/tex]

cosθ = .74

θ  = 42° .  

Answer:

17 m/s

Explanation:

Using formula a = (v-u) /t

acceleration a =  -1.5 m/s2

final velocity v = unknown

initial velocity u = 32 m/s

time t = 10s

-1.5 = (v-32)/10

-15 = v - 32

-15 + 32 = v

v = 17 m/s

Answer:

A. The scale exerts a 17 N force up on the bag.

Explanation:

I Just took the test

Reaction force of the bag sitting on the scale a)The scale exerts a 17 N force up on the bag.

According to newton's third law of motion , every action have a equal and opposite reaction

When bag is being put on the scale to measure its weight , then bag must have exerted a force on the scale , in result of which an equal and opposite force must be exerted by the scale on the bag (according to newton's third law of motion) in order to keep an equilibrium state where both the forces are equal but opposite to each other .

correct option is a)The scale exerts a 17 N force up on the bag.

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Answer:

20.9 volts

Explanation:

R = 27.7 Ω

I = 753 mA = 0.753 A

V = ?

From Ohms law, V = IR

V = 0.753×27.7

V = 20.8581

V = 20.9 volts

Answer:

t = 3.4 s

The box will come to rest in 3.4 s

Explanation:

For the block to come to rest, the friction force must become equal to the unbalanced force. Therefore:

Unbalanced Force = Frictional Force

but,

Unbalanced Force = ma

Frictional Force = μR = μW = μmg

Therefore,

ma = μmg

a = μg

where,

a = acceleration of box = ?

μ = coefficient of sliding friction = 0.45

g = 9.8 m/s²

Therefore,

a = (0.45)(9.8 m/s²)

a = -4.41 m/s²  (negative sign due to deceleration)

Now, for the time to stop, we use first equation of motion:

Vf = Vi + at

where,

Vf = Final Speed = 0 m/s (since box stops at last)

Vi = Initial Speed = 15 m/s

t = time to stop = ?

Therefore,

0 m/s = 15 m/s + (-4.41 m/s²)t

(-15 m/s)/(-4.41 m/s²) = t

t = 3.4 s

The box will come to rest in 3.4 s

Answer:

9,375

Explanation:

Data provided

The mass of the car m = 1500 Kg.

The diameter of the circular track D = 200 m.

For the computation of magnitude and direction of the net force on the car first we need to find out the radius of the circular path which is shown below:-

The radius of the circular path is

[tex]R = \frac{D}{2}[/tex]

[tex]= \frac{200}{2}[/tex]

= 100 m

after the radius of the circular path we can find the magnitude of the centripetal force with the help of below formula

[tex]Force F = \frac{mv^2}{R}[/tex]

[tex]= \frac{1500\times (25)^2}{100}[/tex]

= 9,375

Therefore for computing the magnitude of the centripetal force we simply applied the above formula.

Complete Question

The  complete question(reference (chegg)) is shown on the first uploaded image

Answer:

The magnitude of the resultant force is  [tex]F = 199.64 \ N[/tex]

The  direction of the resultant force is  [tex]\theta = 4.1075^o[/tex] from the horizontal plane

Explanation:

Generally when resolving force, if the force (F )is moving toward the angle then the resolve force will be  [tex]Fcos(\theta )[/tex] while if the force is  moving away from the angle  then the resolved force is  [tex]Fsin (\theta )[/tex]

Now  from the diagram let resolve the forces to their horizontal component

    So

          [tex]\sum F_x = 150 cos(30) + 100cos(15) -80sin (20)[/tex]

          [tex]\sum F_x = 199.128 \ N[/tex]

Now  resolving these force into their vertical component can be mathematically evaluated as

         [tex]\sum F_{y} = 150 sin(30) - 100sin(15) -110 +80 cos(20)[/tex]

         [tex]\sum F_{y} = 14.30[/tex]

Now the resultant force is mathematically evaluated as

        [tex]F = \sqrt{F_x^2 + F_y^2}[/tex]

substituting values

        [tex]F = \sqrt{199.128^2 + 14.3^2}[/tex]

        [tex]F = 199.64 \ N[/tex]

The  direction of the resultant force is  evaluated as

       [tex]\theta = tan^{-1}[\frac{F_y}{F_x} ][/tex]

substituting values

       [tex]\theta = tan^{-1}[\frac{ 14.3}{199.128} ][/tex]

       [tex]\theta = 4.1075^o[/tex] from the horizontal plane

Answer:

4Hz (240 cycles/60 seconds = 4 cycles/second)

Explanation:

hope this helped!

Answer:

  d sin tea = m λ

Explanation:

When we have a two-slit system, the optical path difference determines whether the intensity reaching an observation screen is maximum or zero.

To find this difference in optical path, we assume that the screen is much farther than the gap is, we draw a perpendicular from ray 1 to the second ray

       OP = d sin θ

now to have constructive interference and see a bright line this leg must be an integer number of wavelengths, ose

            d sin tea = m λ

where

d             is the distance between the two slits

θ     complexion the angle sea the point hold it between the two slits

λ    the wavelength of the coherent light used

m   an integer, which counts the number of lines of interference

Units in the SI system

d, lam in meters

θ degrees

m an integer

Answer:

  a = 1.15 10³ g

Explanation:

For this exercise we will use the relations of the centripetal acceleration

     a = v² / r

where is the linear speed of the rotor and r is the radius of the rotor

let's use the relationships between the angular and linear variables

          v = w r

let's replace

          a = w² r

let's reduce the angular velocity to the SI system

        w = 550 rev / min (2pi rad / 1 rev) (1 min / 60 s)

         w = 57.6 rad / s

let's calculate

       a = 57.6²  3.4

       a = 1.13 10⁴ m / s²

To calculate this value in relation to g, let's find the related

       a / g = 1.13 10⁴ / 9.8

       a = 1.15 10³ g

Answer:

103 g

Explanation:

given that

Mass of the attached mass, m = 40 g

Initial distance of balance, x1 = 49.7 cm = 0.497 m

Final distance of balance, x2 = 39.2 cm = 0.392 m

Equilibrium point of attachment, x3 = 14 cm = 0.14 m

To get the mass of the meter stick, we use the relation

M = m.[(x2 - x3) / (x1 - x2)]

And on solving in full, we gave

M = 40.[(0.392 - 0.14) / [0.497 - 0.392)]

M = 40(0.258 / 0.105)

M = 40 * 2.457

M = 102.8 g

Therefore the needed work good for mass of the stick j

Is 103 g

Answer:

When the temperature of the gas is increased from 20 to 40, the pressure will be 2p

Explanation:

Given;

initial temperature of the gas, T₁ = 20 K

final temperature of the gas, T₂ = 40 k

initial pressure of the gas, P₁ = P

final pressure of the gas, P₂ = ?

Apply pressure law of gases;

[tex]\frac{P_1}{T_1} = \frac{P_2}{T_2} \\\\P_2 = \frac{P_1T_2}{T_1} \\\\P_2 = \frac{40P}{20} \\\\P_2 = 2P[/tex]

Therefore, when the temperature of the gas is increased from 20 to 40, the pressure will be 2p

Answer:

Force of Rope = 122.5 N

Force of Rope = 480.2N

Explanation:

given data

length = 3.00 m

mass = 25.0 kg

clown mass = 79.0 kg

angle = 30°

solution

we get here Force of Rope on with and without Clown that is

case (1) Without Clown

pivot would be on the concrete pillar so Force of Rope will be

Force of Rope × 3m = (25kg)×(9.8ms²)×(1.5m)

solve it and we get

Force of Rope = 122.5 N

and

case (2) With Clown

so here pivot is still on concrete pillar and clown is standing on the board middle  and above the centre of mass so Force of Rope will be

Force of Rope × 3m = (25kg+73kg)×(9.8ms²)×(1.5m)

solve it and we get

Force of Rope = 480.2N

Answer:

fb = 240.35 Hz

Explanation:

In order to calculate the beat frequency generated by the first modes of each, organ and tube, you use the following formulas for the fundamental frequencies.

Open tube:

[tex]f=\frac{v_s}{2L}[/tex]         (1)

vs: speed of sound = 343m/s

L: length of the open tube = 0.47328m

You replace in the equation (1):

[tex]f=\frac{343m/s}{2(0.47228m)}=362.36Hz[/tex]      

Closed tube:

[tex]f'=\frac{v_s}{4L'}[/tex]

L': length of the closed tube = 0.702821m

[tex]f'=\frac{343m/s}{4(0.702821m)}=122.00Hz[/tex]

Next, you use the following formula for the beat frequency:

[tex]f_b=|f-f'|=|362.36Hz-122.00Hz|=240.35Hz[/tex]

The beat frequency generated by the first overtone pf the closed pipe and the fundamental of the open pipe is 240.35Hz

Answer:

(a) v1 = 21.6 m/s

(b) t = 51.25 s

Explanation:

Use kinematics equation

v1 = v0 + at

Given

v0 = 0 = initial velocity

a = 0.8 m/s^2 = acceleration

(a) t = 27 seconds

v1 = v0 + at = 0 + 0.8*27 = 21.6 m/s

(b) v1 = 41 m/s

v1 = v0 + at

solve for t

t = (v1-v0)/a = (41-0)/0.8 = 51.25 s

Given:

By using Kinematics equation, we get

→ [tex]v_1 = v_0+at[/tex]

(a)

At t = 27 seconds,

→ [tex]v_1 = v_0 +at[/tex]

       [tex]= 0+0.8\times 27[/tex]

       [tex]= 21.6 \ m/s[/tex]

(b)

When [tex]v_1 = 41 \ m/s[/tex]  

→ [tex]t = \frac{(v_1-v_0)}{a}[/tex]

     [tex]= \frac{41.0}{0.8}[/tex]

     [tex]= 51.25 \ s[/tex]

Thus the response above is right.

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Answer:

0.00299T

Explanation:

The magnetic field B = 0.00299T

The  lens is designed to work in the visible, near-infrared, and near-ultraviolet. The best resolution of this lens from a diffraction standpoint is: in the near-ultraviolet.

The act of bending light around corners such that it spreads out and illuminates regions where a shadow is anticipated is known as diffraction of light. In general, since both occur simultaneously, it is challenging to distinguish between diffraction and interference. The diffraction of light is what causes the silver lining we see in the sky. A silver lining appears in the sky when the sunlight penetrates or strikes the cloud.

Longer wavelengths of light are diffracted at a greater angle than shorter ones, with the amount of diffraction being dependent on the wavelength of the light. Hence, among the light waves of  the visible, near-infrared, and near-ultraviolet range, near-ultraviolet waves have the shortest wavelengths. So,  The best resolution of this lens from a diffraction standpoint is in the near-ultraviolet, where diffraction is minimum.

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Answer:

The current and the applied emf can be in phase if either of the two changes are made.

1) The inductance of the inductor is doubled, with everything else remaining constant.

2) The capacitance of the capacitor is doubled, with everything else remaining constant.

Explanation:

The current and applied emf for this type of circuit would be in phase when there is no phase difference between the two quantities. That is, Φ = 0°.

The phase difference between current and applied emf is given as

Φ = tan⁻¹ [(XL - Xc)/R]

XL = Impedance due to the inductor

Xc = Impedance due to the capacitor

R = Resistance of the resistor.

For Φ to be 0°, tan⁻¹ [(XL - Xc)/R] = 0

But only tan⁻¹ 0 = 0 rad

So, for the phase difference to be 0,

[(XL - Xc)/R] = 0

Meaning

XL = Xc

But for this question,

XL = 100 Ω, Xc = 200 Ω

For them to be equal, we have to find a way to increase the impedance of the inductor or reduce the impedance of the capacitor.

The impedance are given as

XL = 2πfL

Xc = (1/2πfC)

f = Frequency

L = Inductance of the inductor

C = capacitance of the capacitor

The impedance of the inductor can be increased from 100 Ω to 200 Ω by doubling the inductance of the inductor.

And the impedance of the capacitor can be reduced from 200 Ω to 100 Ω by also doubling the capacitance of the capacitor.

So, these are either of the two ways to make the current and applied emf to be in phase.

Hope this Helps!!!

Answer:

Seismic attenuation describes the energy loss experienced by seismic waves as they propagate. It is controlled by the temperature, composition, melt content, and volatile content of the rocks through which the waves travel.

Explanation:

Answer:

5.724 meters / second^2

Explanation:

We are given two pieces of information, 5.24 flurg = 1 meter, 1 grom = 0.493 second. If that is so, we can say that there are two possible conversion units,  5.25 flurg / meter, and 0.493 second / grom.

_____

We want to convert 7.29 flurg / grom^2 ( I believe? ) to the units meters / second^2. But, let's break this down into bits. It would be convenient to first convert 7.29 flurg / grom^2 to the units meters / grom^2, by dividing the conversion factors as to cancel out the appropriate things, which we will go into detail on a bit later ( using the first conversion factor ). Respectively we can convert meters / grom^2 to meters / grom * s, canceling out the flurg ( through the second conversion factor ). And now we would need to get rid of the grom, dividing similarly.

_____

( 1 ) ( flurg / grom^2 ) / ( flurg / meters  ) - first conversion unit

= flurg / grom^2 * meters /flurg

= ( meters * flurg ) / ( grom^2 * flurg )  

= meters /grom^2,

7.29 flurg / grom^2 / 5.24 flurg / meter = ( About ) 1.39 meter / grom^2

( 2 ) ( meter / grom^2 ) / ( second / grom  ) - second conversion unit

= meter / grom^2 * grom / second

= ( meter * grom ) / ( grom^2 * second )

= meter / ( grom * second ),

( 1.39 meter / grom^2 ) / 0.493 second / grom = ( About ) 2.82195 meter /  grom * second

( 3 ) ( 2.82195 meter / ( grom * second ) ) / 0.493 second / grom = 5.724 meter / second^2

( And thus, the value of gOP7 in the units the architects will use should be about 5.724 meters / second^2 )

The value of gOP7 in the units your architects will use is 5.724 [tex]m/s^2[/tex]

Given that 5.24 flurg = 1 meter,

1 grom = 0.493 second.  

First, we will convert the length units:

[tex]7.29 flurg / grom^2 / 5.24 flurg / meter = 1.39 meter / grom^2[/tex]

Now we convert the time units:

[tex]1.39 meter / grom^2 / 0.493 second / grom = 2.82195 meter / grom * second[/tex]

 [tex]2.82195 meter / ( grom * second ) ) / 0.493 second / grom = 5.724 meter / second^2[/tex]

The value of gOP7 in the units the architects will use is [tex]5.724m/s^2[/tex]

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Complete Question

A commuter train passes a passenger platform at a constant speed of 39.6 m/s. The train horn is sounded at its characteristic frequency of 350 Hz.

(a)

What overall change in frequency is detected by a person on the platform as the train moves from approaching to receding

(b) What wavelength is detected by a person on the platform as the train approaches?

Answer:

a

  [tex]\Delta f = 81.93 \ Hz[/tex]

b

  [tex]\lambda_1 = 0.867 \ m[/tex]

Explanation:

From the question we are told that

      The speed of the train is  [tex]v_t = 39.6 m/s[/tex]

      The frequency of the train horn is  [tex]f_t = 350 \ Hz[/tex]

Generally the speed of sound has a constant values of  [tex]v_s = 343 m/s[/tex]

  Now  according to dopplers equation when the train(source) approaches a person on the platform(observe) then the frequency on the sound observed by the observer can be mathematically represented as  

        [tex]f_1 = f * \frac{v_s}{v_s - v_t}[/tex]

substituting values

        [tex]f_1 = 350 * \frac{343 }{343-39.6}[/tex]

       [tex]f_1 = 395.7 \ Hz[/tex]

  Now  according to dopplers equation when the train(source) moves away from  the  person on the platform(observe) then the frequency on the sound observed by the observer can be mathematically represented as  

           [tex]f_2 = f * \frac{v_s}{v_s +v_t}[/tex]

substituting values

        [tex]f_2 = 350 * \frac{343}{343 + 39.6}[/tex]

       [tex]f_2 = 313.77 \ Hz[/tex]

The overall change in frequency is detected by a person on the platform as the train moves from approaching to receding is mathematically evaluated as

        [tex]\Delta f = f_1 - f_2[/tex]

        [tex]\Delta f = 395.7 - 313.77[/tex]

        [tex]\Delta f = 81.93 \ Hz[/tex]

Generally the wavelength detected by the person as the train approaches  is mathematically represented  as

          [tex]\lambda_1 = \frac{v}{f_1 }[/tex]

          [tex]\lambda_1 = \frac{343}{395.7 }[/tex]

         [tex]\lambda_1 = 0.867 \ m[/tex]

Answer:

a) 238U, 40K and 87Rb, b)   235U and to a lesser extent 40K , c)  he 235U,

d) possibility is 14C , e)this period would be ideal for 14C , f) 14C should be used since it is the one with the least average life time, even though the measurements must be very careful

Explanation:

One of the applications of radioactive decay is the dating of different systems.

To do this, the quantity of radioactive material in a meter is determined and with the average life time, the time of the sample is found.

Let's write the half-life times of the given materials

87Rb T ½ = 4.75 1010 years

147Sm T ½ = 1.06 1011 years

235U = 7,038 108 years

238U = 4.47 109 years

40K = 1,248 109 years

14C = 5,568 103 years

we already have the half-life of the different elements given

a) meteors. As these decomposed in the formation of the solar system, their life time is around 3 109 to 5 109 years, so it is necessary to look for elements that have a life time of this order, among the candidates we have 238U, 40K and 87Rb if these elements were at the moment of the formation of these meteors, there must still be rations in them, instead elements 14C already completely adequate

b) rock. The formation period is 4.20-108 years, therefore one of the most promising elements is 235U and to a lesser extent 40K since it is more abundant in rocks. The other elements with higher life times have not decayed and therefore will not give a true value and the 14C is completely decayed

c) volcanic ash. Formation time 6107 years, the only element that has the possibility of having a count is the 235U, the others have a life time so long that they have not decayed and the 14C is complete, unbent

d) scarp of an earthquake formation time 5 101 years, The only one that has any possibility is 14C even when it has declined very little, all the others, you have time to long that has not decayed

e) INCA excavation. The time of this civilization is about 10000 to 500 years (104 to 5 102 years), we see that this period would be ideal for 14C since it has some period of cementation, the others have not decayed

f) Tree in Blepharitis. 14C should be used since it is the one with the least average life time, even though the measurements must be very careful because of a period of disintegration. We have such a long time that they have not decayed

Answer:

5

Explanation:

Count the number of moles of O in the product side:

3x2 + 4

= 10

Divide it by 2 since O exists as diatomic molecule (O2)

10/2 = 5

Therefore, the coefficient required is 5.

Answer:

c.) 5

Explanation:

Answer:

The definition of that same given problem is outlined in the following section on the clarification.

Explanation:

The Q seems to be endless (hardly any R on the circuit). So energy equations to describe and forth through the inducer as well as the condenser.  

Presently take a gander at the energy stored in your condensers while charging is Q.

⇒  [tex]U =\frac{Qmax^2}{C}[/tex]

So conclude C doesn't change substantially as well as,

When,

⇒  [tex]Q=\frac{Qmax}{2}[/tex]

⇒  [tex]Q^2=\frac{Qmax^2}{4}[/tex]

And therefore only half of the population power generation remains in the condenser that tends to leave this same inductor energy at 3/4 U.

Answer:

Increasing population

Explanation:

As we can see that the death rate is decreasing while at the same time the birth rate is increasing due to which it increased the population that directly impact the planet so great

Day by day the population of the villages, cities, states, the country is increasing which would create a direct human impact on the planet  

Therefore the increasing population is the one and single most important reason

Answer:

b. only ray that reflects back in the same direction it came from

Explanation:

C-rays can be said to be a ray that comes from the center of the curvature. It is known that any ray that comes from the center of the curvature reflects back in the same direction it came from, this is because the line joining from the center of the curvature to any point in the mirror is perpendicular to the mirror.

Correct answer is option B.

C-ray is the only ray that reflects back in the same direction it came from.

Option A is incorrect because for other rays, angle of incidence = angle of reflection. This is not a property of c-ray.