A wrench is used to apply a torque to a bolt. Forces F1 through F6 all have the same magnitude. The point of application of force Fi (and F) is a distance d from the center of rotation of the bolt. The application points of Fı, F2, and F3 are all distance d apart, as shown. Use the convention that counter-clockwise torques are positive; clockwise torques are negative.
Part (a) Which of the labeled forces will apply the largest magnitude torque on the bolt? O All forces apply the same torque. O F1 O F4 O F3
O F2 O F5
O F6

The symbol for a variable resistor is a line with a zig zag pattern with a diagonal line drawn across it.

What is a variable resistor ?

A resistor whose electric resistance value may be altered is known to as a variable resistor. A variable resistor, which works usually by sliding a contact (wiper) over a variable resistor, is basically an electro-mechanical transducer.

The flow of electrical current is restricted by a resistor. The resistivity of a fixed resistor is steady. By adjusting a slider's position, the resistance of this resistor can be altered. Some volume controls and dimmer switches employ variable resistors.

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The magnitude of the force that the beam exerts on the hi.nge will be,261.12N.

To find the answer, we need to know about the tension.

                           [tex]N_x=86.62N[/tex]

                           [tex]N_y=F_V=mg-Tsin59\\[/tex]

                           [tex]F_H=N_x=Tcos59\\\\T=\frac{F_H}{cos59} =\frac{86.62}{0.51}= 169.84N[/tex]

                    [tex]N_y= (40*9.8)-(169.8*sin59)=246.4N[/tex]

                 [tex]N=\sqrt{N_x^2+N_y^2} =\sqrt{(86.62)^2+(246.4)^2}=261.12N[/tex]

Thus, we can conclude that, the magnitude of the force that the beam exerts on the hi.nge is 261.12N.

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The hi.nge will be subjected to a force of 261.12N from the beam.

We must understand the tension in order to choose the solution.

                       [tex]N_y=F_v=mg-Tsin59[/tex]

                         [tex]F_H=N_x=Tcos59\\T=\frac{F_H}{cos59} =169.84N[/tex]

                  [tex]N_y=(40*9.8)-(169.84*sin59)=246.4N[/tex]

                        [tex]N=\sqrt{N_x^2+N_y^2} =261.12N[/tex]

Thus, we can infer that the force the beam applies to the height is 261.12N in size.

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The stiffness constant of the spring is 68,290.3 N/m

Apply the principle of conservation of energy;

U = K.E

¹/₂kx² = ¹/₂mv²

kx² = mv²

k = mv²/x²

where;

k = (1300 x 16.67²)/(2.3²)

k = 68,290.3 N/m

Thus, the stiffness constant of the spring is 68,290.3 N/m.

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Answer:

90.3N

Explanation:

⊥mg = (0.170 m)(1.20 kg) 9.81 m/s

τ ball = r⊥Wball = (0.340 m)(1.42 N) = − 0.483 N ⋅m

F − 2.001− 0.483 N ⋅m = 0

F = 2.484 N ⋅m

0.0275 m = 90.3 N

The net torque acting on the forearm and hand is 90.3N

Torque is a measure of the pressure that can motivate an object to rotate about an axis. simply as pressure is what causes an object to accelerate in linear kinematics, torque is what reasons an item to collect angular acceleration. Torque is a vector amount.

⇒mg = (0.170 m)(1.20 kg) 9.81 m/s

⇒torque = r⊥weight of the ball

⇒ (0.340 m)(1.42 N) = − 0.483 N ⋅m

⇒F = − 2.001− 0.483 N ⋅m = 0

⇒F = 2.484 N ⋅m

⇒0.0275 m = 90.3 N

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(a) The minimum force F he must exert to get the block moving is 38.9 N.

(b) The acceleration of the block is 0.79 m/s².

The minimum force F he must exert to get the block moving is calculated as follows;

Fcosθ = μ(s)Fₙ

Fcosθ = μ(s)mg

where;

F = [0.1(36)(9.8)] / [(cos(25)]

F = 38.9 N

F(net) = 38.9 - (0.03 x 36 x 9.8) = 28.32

a = F(net)/m

a = 28.32/36

a = 0.79 m/s²

Thus, the minimum force F he must exert to get the block moving is 38.9 N.

The acceleration of the block is 0.79 m/s².

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1.06 is the maximum refractive index that the liquid may have for the light to be totally reflected.

Only when a light source passes from a denser to a rarer medium can it completely reflect.

When the angle of incidence surpasses a specific critical value, specular reflection occurs in the more highly refractive of the two mediums at their interface, and this reflection is known as total reflection.

sin [tex]i_{c}[/tex] = μ[tex]_{r}[/tex] / μ[tex]_{d[/tex]

From the diagram

Angle of incidence = 60°

sin60°  ≥ sin[tex]i_{c}[/tex] = μ[tex]_{r}[/tex]/μ[tex]_{d}[/tex]

μ[tex]_{r}[/tex] ≤ μ[tex]_{d}[/tex] sin60°

μ[tex]_{r}[/tex] ≤ √1.5 × √3/2

   = 1.06

Hence, the maximum index that the liquid may have for the light to be totally reflected is 1.06

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The number of half-lives that would go by in 44 h is 7 half-lives

This is the time taken for half a substance to decay

The number of half-lives that will elaspe after 44 h can be obtained as illustrated below:

n = t / t½

n = 44 / 6.01

n = 7

Thus, 7 half-lives will elaspe after 44 h

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The minimum speed required for a satellite in order to break free permanently from the planet and the radius of the synchronous orbit of a satellite are 7.3 Km/s and 3.1 × 10⁴ km respectively.

To find the answer, we need to know about the escape velocity and time period of revolving satellite.

          = 7.3 Km/s

        = 3.1 × 10⁴ km

Thus, we can conclude that the escape velocity and the radius of the synchronous orbit of a satellite are 7.3 Km/s and 3.1 × 10⁴ km respectively.

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The force exerted per square centimeter is 126 N/cm².

Pressure is the force acting per unit area.

Based on the data given:

volume increase, ΔV/V0 = 6 * 10⁻³

Bulk Modulus, B = 2.1 * 10⁹ N/m²

Bulk modulus B of a material is ratio of change in pressure and change in volume as given below:

Solving for ΔP;

ΔP = B * [(ΔV/V)]

ΔP = (2.1 * 10⁹ N/m²) * (6 * 10⁻³)

ΔP = 1.26 * 10⁶ N/m²

Converting to per square centimeter

ΔP = (1.26 * 10⁶ N/m²)/10⁴

ΔP = 126 N/cm²

In conclusion, the force exerted per square centimeter is a measure of the pressure.

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The mechanical energy lost is 353.28 Joules . The distance he slid off is 0.16m.

we know:-

Mass = 69 kg

Speed = 3.2 m/s

Coefficient of friction ( ratio of friction force and normal force ) = 0.70

Acceleration due to gravity, g = 9.8 m/s^2

(a) To determine the amount of mechanical energy that is lost because of friction acting on the runner, we would calculate the change in kinetic energy:

[tex]KE = \frac{1}{2} m (v-u)^{2}[/tex]

      [tex]= \frac{1}{2} 69 ( 3.2-0 )^{2}[/tex]

      [tex]= 353.28[/tex] Joules

Mechanical energy = 353.28 Joules

(b) To determine how far (distance) the runner slide:

acceleration = ug

                     [tex]= 3.2[/tex] × [tex]9.8[/tex]

                     [tex]= 31.36[/tex] [tex]m/s^{2}[/tex]

distance ,

[tex]V^{2} = U^{2} + 2aS[/tex]

[tex]( 3.2)^{2} = 0 + 2 ( 31.36) S[/tex]

[tex]10.24 = 62.72 S[/tex]

[tex]S = {\frac{10.24}{62.72} }[/tex]

Distance, S = 0.16 m  

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Answer:

I think it's force

Explanation:

Mark as brainliest if it is right

Answer: A

Explanation:

Force can cause a stationary object to start moving or a moving object to change its speed or direction or both

The vertical component of the force exerted by the hi.nge on the beam is 114.77 N.

Apply the principle of moment and calculate the tension in the cable;

Clockwise torque = TL sinθ

Anticlockwise torque = ¹/₂WL

TL sinθ  =  ¹/₂WL

T sinθ  =  ¹/₂W

T = (W)/(2 sinθ)

T = (29 x 9.8)/(2 x sin57)

T = 169.43 N

T + F = W

F = W - T

F = (9.8 x 29) - 169.43

F = 114.77 N

Thus, the vertical component of the force exerted by the hi.nge on the beam is 114.77 N.

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The  energy she has at each position shown are:

Velocity is known to be a term that connote the direction of any kind of a moving body or an object.

Note that the Speed is known to be a a scalar quantity and as such,  Velocity is said to be a vector quantity.

Note also that from the question given,  Jessica's height of the swing 3 meters above the ground, therefore:

Jessica Position at maximum height :

PE = mgh

PE = 44kg x  9.8m/s² x 3

PE = 1,294 J

Jessica  Position at minimum height:

PE = 0 J

Jessica  Position at maximum velocity:

KE = 1/2 x mv²

KE = 1/2 x 44kg x (5m/s²)²

KE = 550 J

Jessica  Position at minimum velocity:

KE = 0 J

Therefore, The  energy she has at each position shown are:

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(a) The tension the musician must stretch it is 147.82 N.

(b) The percent increase in tension is needed to increase the frequency is 26%.

v = √T/μ

where;

v = Fλ

in fundamental mode, v = F(2L)

v = 2FL

v = 2 x 65.4 x 0.6 = 78.48 m/s

v = √T/μ

v² = T/μ

T = μv²

T = 0.024 x (78.48)²

T = 147.82 N

v = 2FL = 2 x 73.4 x 0.6 = 88.08 m/s

T = μv²

T = (0.02)(88.08)²

T = 186.19 N

= (186.19 - 147.82)/(147.82)

= 0.26

= 0.26 x 100%

= 26 %

Thus, the tension the musician must stretch it is 147.82 N.

The percent increase in tension is needed to increase the frequency is 26%.

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These given conditions satisfy the second law of thermodynamics.

As the process is isobaric

So there will be a straight line of P= 200kPa in P-v and P-T planes

P1 = P2 = 100kPa

For perfect ideal gas, v-T plane:

[tex]v = (\frac{R}{P}) T[/tex]

[tex]v_{1} = (\frac{R}{P_{1} }) T_{1}[/tex] = 287 × 500/200000 = 0.717 m³/kg

[tex]v_{2} = (\frac{R}{P_{2} }) T_{2}[/tex] = 287 × 600/200000 = 0.861m³/kg

As it is the calorically perfect gas

de = [tex]c_{v}[/tex]dT

Integration on both sides

e2 - e1 = [tex]c_{v}[/tex](T2 - T1)

           = ( 716.5J/kg/K) (600-500)

           = 71650 J/kg

also,

Tds = de + Pdv

Tds = [tex]c_{v}[/tex]dT +Pdv

For ideal gas

V = RT/P        

dv = Rdt/P - RTdp/P²

Tds = [tex]c_{v}[/tex]dT + Rdt - RTdp/P

ds = ([tex]c_{v}[/tex] + R)dT/T - RdP/P

ds = ([tex]c_{v} + c_{p} -c_{v}[/tex])dT/T - RdP/P

ds = [tex]c_{p}[/tex]dT/T - RdP/P

Integration on both sides

s2 - s1 = [tex]c_{p}[/tex]ln (T2/T1) - R ln (P2/P1)

Since P is constant

s₂ - s₁ = [tex]c_{p}[/tex] ln (T2/T1)

           = 1003.5 ln (600/500)

           = 1003.5 × 0.182

           = 182.95 J/kg/K

w = Pdv

[tex]w_{12}[/tex] = P(v₂ - v₁)

     = 2,00,000 ( 0.861 - 0.717)

     = 28,800 J/kg

de = δq -δw

δq = de + δw

q₁₂ = (e₂ - e₁) +  w₁₂

    =  71,650 + 28,800 = 1,00,450 J/kg

Now in this process, the gas is heated from 500 K to 600 K. We would expect at a minimum that the surroundings were at 600 K.

Let’s check for second law satisfaction.

s₂ - s₁ ≥ q₁₂ / Tₓ

182.95 ≥ 1,00,450 / 600 K

182.95 J/kg/K ≥ 167.41 J/kg/K

Hence this condition satisfies the second law of thermodynamics

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The angular speed of the merry-go-round just after the child has jumped onto it is 0.696 rad/s.

The principle of conservation of angular momentum states that the sum of initial angular momentum is equal to final angular momentum.

Li = Lf

Li = Ii ωi  + Ic ωc

Li = Iiωi  +  MR²(V/R)

Li =  Iiωi + MRV ----- (1)

Lf = If ωf

ωf = Lf/If

If = Im  + MR²

ωf = Lf / ( Im  + MR²)

Recall, Lf = Li

ωf = (Iiωi + MRV) / ( Im  + MR²)

where;

ωf = (Iiωi + MRV) / ( Im  + MR²)

ωf = (0 + 40 x 1.5 x 8) / (600 + 40(1.5)²)

ωf = (480) / (690)

ωf = 0.696 rad/s

Thus, the angular speed of the merry-go-round just after the child has jumped onto it is 0.696 rad/s.

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Answer:

12 grams of the isotope carbon-12.

Explanation:

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Answer:

Object A's momentum is larger

Explanation:

as the formula for momentum goes:

P = M * V

where P is momentum, M is mass, V is velocity.

so where Va (Object A's velocity) is larger than Vb (Object B's velocity) we get:

( i ) Va > Vb

as the masses of both objects are equal, we mark:

( ii) Ma = Mb = M

we multiply both sides of ( i ) by M to get:

( iii ) Va × M > Vb × M

and we finally get:

( iv ) Pa > Pb

Answer: Object A's momentum of larger than compared to that of object B.

Explanation:

Tension in the rope C is 1.24× 10² N.

To find the answer, we need to know about the horizontal component of tension in the rope B.

Horizontal component= tension in rope B × cos80.5°

= 7.52×10² N × cos80.5°

= 1.24×10² N

Thus, we can conclude that the tension in the rope C is 1.24× 10² N.

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The minimum necessary height of the IV bag above the position of the needle, if the density of the solution is 1.308kg/L, and the pressure in the vein is 35.7 mmHg is, 2.78m.

To find the answer, we need to know more about the pressure exerted by a liquid column.

                                                [tex]P=[/tex] ρgh

                                           [tex]density=1.308 kg/L\\\\P=35.7 mmHg.\\[/tex]

                                       [tex]h=\frac{P}{density*g} =\frac{35.7}{1.308*9.8}\\\\ h=2.78 m[/tex]

Thus, we can conclude that, the height of the Iv bag is 2.78 m above the position of needle.

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If the solution has a density of 1.308 kg/L and the vein pressure is 35.7 mmHg, the minimum height of the IV bag above the needle position is 2.78 m.

We need to learn more about the pressure that a liquid column exerts in order to determine the solution.

                            [tex]P=[/tex] ρgh

                        [tex]Density=1.308kg/L\\P=35.7mmHg[/tex]

                           [tex]h=\frac{P}{density*g}\\\\ h=2.78m[/tex]

As a result, we may say that the I.V. bag is 2.78 m above the ground.

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The ratio of the speed of the lighter bullet to the speed of the heavier will be four times the heavier bullet.

Both can do same amount of work.

Kinetic energy of a body is the energy due to the motion of the body.

Kinetic energy = mv²/2

where m is mass and v is velocity of the object.

Since both objects have the same kinetic energy but one bullet has twice the mass of the other, the ratio of the speed of the lighter bullet to the speed of the heavier will be four times the heavier bullet.

The kinetic energy of both bullets is the same. Hence, they can do equal amount of work.

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Based on the calculations, the sound intensity level is equal to 1.0 × 10⁻⁵ W/m².

Mathematically, sound intensity level can be calculated by using this formula:

[tex]\beta = 10 log(\frac{I}{I_{ref}} )[/tex]

Where:

I is the intensity of the sound.

Note: The reference value of sound intensity is equal to 1.0 × 10⁻¹² W/m².

Rewriting the formula, we have:

β/10 = logI - logIo

Substituting the parameters into the formula, we have;

60/10 = logI - log(1.0 × 10⁻¹²)

6 = logI + 12

logI = 6 - 12

logI = -6

I = 1.0 × 10⁻⁵ W/m².

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The direction of magnetic field is south-east and the magnitude is

[tex]23.66[/tex] × [tex]10^{3} N/C[/tex].

Here, the magnitude of CD and BC will be cancelled, as they both are in the opposite direction and equal to each other.
the magnitude, towards the diagonal AC will result in CP, which is the direction of the electric field.

magnitude of electric field can be defined as :- The force per charge on the test charge is a straight forward way to define the size of the electric field.

To find the magnitude of the electric field use the formula

[tex]E = kq/ r^{2}[/tex]

inserting the values,

[tex]E = 9. 10^{9}[/tex] × [tex]4.05[/tex] × [tex]10^{-6} / 1.1 \sqrt{2}[/tex]

[tex]E= 36.45[/tex] × [tex]10^{3}[/tex] / [tex]1.54[/tex]

[tex]E = 23.66[/tex] × [tex]10^{3}[/tex] N/C

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The mass of the airplane of area of two wings 395m², and the average speed of lower and upper surface of the wings are, 259 and 288m/s is 386.8×10^3 kg.

To find the answer, we need to know about the Bernoulli's principle.

                   P+ [tex]\frac{1}{2}[/tex] ρv²+ρgh=a constant.

Instead of ρ we take d as density.

                    [tex]A= 395 m^2\\v_l=295 m/s\\v_u=288m/s\\density=1.21kg/m^3[/tex]

                     [tex]P_1+\frac{1}{2}v_1^2d+dgh_1=P_2+ \frac{1}{2}v_2^2d+dgh_2\\here\\h_1=h_2\\thus\\P_1-P_2=\frac{1}{2}d(v_2^2-v_1^2)\\P_1-P_2=\frac{1}{2}*1.21(288^2-259^2)=9597.12 atm\\[/tex]

                       [tex]\frac{F}{A}=9597.12 atm\\\\ F=9597.12*395m^2=37.9*10^5 N\\\\mg=37.9*10^5 N\\\\m=\frac{37.9*10^5 N}{9.8}\\\\ m=386.8*10^3kg[/tex]

Thus, we can conclude that, the mass of the airplane is 386.8×10^3 kg.

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The mass of an airplane with two wings that are 395m2 in size and average wing surface speeds of 259 and 288 m/s is 387x 10^3 kg.

We need to be aware of the Bernoulli principle in order to determine the solution.

                             P+ [tex]\frac{1}{2}[/tex]dv²+dgh = constant.

We substitute d for to represent density.

                           [tex]v_1=259m/s\\v_2=288m/s\\A=395m^2\\d=1.21kg/m^3[/tex]

                            [tex]P_1+\frac{1}{2}dv_1^2+dgh= P_2+\frac{1}{2}dv_2^2+dgh\\\\P_1+\frac{1}{2}dv_1^2=P_2+\frac{1}{2}dv_2^2\\\\P_1-P_2=\frac{1}{2}d(v_2^2-v_1^2)\\\\P_1-P_2=9597 atm[/tex]

                        [tex]F/A= 9597 atm\\mg=9597*395 =38*10^5N\\m=\frac{38*10^5}{9.8} = 387*10^3kg[/tex]

Consequently, we can say that the mass of an airplane with two wings that are 395m2 in size and average wing surface speeds of 259 and 288 m/s is 387 x 10^3 kg.

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Answer:

more durability and easier to pound a hammer with the heavy weight.

Explanation:

One should use an iron hammer instead of the wooden hammer because the force developed with the help of the iron hammer is far greater than the wooden hammer

Newton's Second Law states that The resultant force acting on an object is proportional to the rate of change of momentum.

The mathematical expression for Newton's second law is as follows

F = m*a

where F represents the force applied

m is the mass of the object

a is the acceleration of the object

As we know that force is a product of mass and acceleration, let us assume that both iron and wooden hammers have the same dimension , considering the acceleration applied is the same while hammering ,

As for the same dimension the mass of iron hammer would be greater as result force applied through the iron hammer would be grater

Since the iron hammer's force is so much stronger than the wooden hammer's force, one should use an iron hammer instead of a wooden hammer.

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The minimum  necessary height of the IV bag above the position of the needle is 0.37 m.

we know that,

P = ρgh

where,

P = 35.7mmHg

  = 4759.609 Pa

g = 9.8[tex]\frac{m}{s^{2} }[/tex]

ρ = 1.308 kg / m^3

now, substituting all the values, we get,

4759.609 = 1.308 × 9.8 × h

h = 0.37 m

The minimum  necessary height of the IV bag above the position of the needle = 0.37 m.

what is an IV bag ?

A reagent, also called as an analytical reagent, is a substance or compound that is added to a system in chemistry to bring about a chemical reaction or examine to see if one happens. Even though the terms "reagent" and "reactant" are frequently used synonymously, "reactant" refers to a substance that is consumed during a chemical reaction.

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A round cactus with many spines is the adaptation of a cactus that protects it from predators.

A cactus, unlike other plants, has unique adaptations in its roots, leaves, and stems that allow it to flourish in hot and dry surroundings.

The one adaptation that protects the cactus from predators is spines.

A cactus does not have any parts that resemble leaves if you could look at one closely.

Instead, the leaves are transformed into spines, which protrude from the plant's tiny bumps known as areoles.

Herbivores that live in the desert may be enticed to eat the cactus. The spines prevent these predators by modifying leaves into spines.

Other than protection, Spines perform many functions like

1) Since evaporation is a problem in a desert since water is scarce, the spines prevent excessive evaporation.

2)  The spines also impede airflow and prevent evaporation by trapping air.

3) Collecting dew from the early-morning fog is another crucial job that the spines do.

The gathered dew turned into liquid water and ran down to the earth below. The plant then absorbs this water.

Hence, the adaptation of a cactus that protects it from predators is round cactus with many spines.

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No. of turns in the solenoid is an option (b) 144.

The self-inductance of a long solenoid depends only on its physical properties (such as the number of turns of wire per unit length and the volume), and not on the magnetic field or the current.

Self-inductance of solenoid = 39.1 μH

                                           = 39.1 × [tex]10^-^6[/tex] H

Length of the solenoid = 4.0 cm

Cross-sectional area = 0.60 cm²

Expression for the self-inductance of a coil ;

L = µ₀N²A / [tex]l[/tex]

where,

L = Self- Inductance

N = No. of turns.

A = Cross-sectional area

[tex]l=[/tex] Length of the solenoid

L =( 4π × [tex]10^-^7[/tex] × N² × 0.60 ) / 4.0

39.1× 4.0 / 4π × [tex]10^-^7[/tex] × 0.60 = N²

N² = 2.07 × [tex]10^6[/tex]

N = 144

Therefore, the no. of turns of the solenoid is 144.

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An object with a velocity (v) of 9 m/s and a linear momentum (p) of 72 kg.m/s, has a mass (m) of 8 kg.

In Newtonian mechanics, linear momentum, or simply momentum, is the product of the mass and velocity of an object.

It is a vector quantity, possessing a magnitude and a direction.

The mathematical expression for momentum is:

p = m . v

where,

An object has a velocity (v) of 9 m/s and its linear momentum (p) is 72 kg.m/s. We will use the definition of linear momentum to calculate the mass of the object.

p = m . v

m = p / v

m = (72 kg.m/s) / (9 m/s) = 8 kg

An object with a velocity (v) of 9 m/s and a linear momentum (p) of 72 kg.m/s, has a mass (m) of 8 kg.

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