Pascal's principle says: a A change in pressure at one point in an incompressible fluid is felt at every other point in the fluid. b The buoyant force equals the weight of the displaced fluid. c Matter must be conserved in a flowing, ideal fluid. d Energy is conserved in a flowing, ideal fluid. e A small input force causes a large output force.

Answer:

v=26.23*105 m/s

or 2.6 × 106 m/s

Explanation:

Force generated by magnetic field will only provide centripetal acceleration thus the entering speed will be same as the exit speed

so,

.5mv2=eV potential differnce*charge= kinetic energy

.5*35*1.66*10-27*v2= 1.6*10-19*5*250000

v2=68.84*1011

v=26.23*105 m/s

or 2.6 × 106 m/s

Answer:

ΔU  = e(V₂ - V₁) and its value ΔU = -2.275 × 10⁻²¹ J

Explanation:

Since the electric potential at point 1 is V₁ = 33 V and the electric potential at point 2 is V₂ = 175 V, when the electron is accelerated from point 1 to point 2, there is a change in electric potential ΔV which is given by ΔV = V₂ - V₁.

Substituting the values of the variables into the equation, we have

ΔV = V₂ - V₁.

ΔV = 175 V - 33 V.

ΔV = 142 V

The change in electric potential energy ΔU = eΔV = e(V₂ - V₁) where e = electron charge = -1.602 × 10⁻¹⁹ C and ΔV = electric potential change from point 1 to point 2 = 142 V.

So, substituting the values of the variables into the equation, we have

ΔU = eΔV

ΔU = eΔV

ΔU = -1.602 × 10⁻¹⁹ C × 142 V

ΔU = -227.484 × 10⁻¹⁹ J

ΔU = -2.27484 × 10⁻²¹ J

ΔU ≅ -2.275 × 10⁻²¹ J

So, the required equation for the electric potential energy change is

ΔU  = e(V₂ - V₁) and its value ΔU = -2.275 × 10⁻²¹ J

Answer:

3.1 kg

Explanation:

Applying,

R = m(g-a)..................... Equation 1

Where R = weight of the scale when the elevator is coming down, a = acceleration of the elevator, g = acceleration due to gravith.

From the question,

Given: m = 5 kg, a = 3.8 m/s²

Constant: g = 9.8 m/s²

Substitute these values into equation 1

R = 5(9.8-3.8)

R = 5(6)

R = 30 N

Hence the spring scale is

m' = R/g

m' = 30/9.8

m' = 3.1 kg

Answer:

Hydraulic brake systems are used as the main braking system on almost all passenger vehicles and light trucks. Hydraulic brakes use brake fluid to transmit force when the brakes are applied.

Explanation:

Answer:

350

Explanation:

Since it travels 350 meters per second, the jet will travel 350 meters in one second.

Answer:

[tex]dF=2.5Hz[/tex]

Explanation:

From the question we are told that:

Time [tex]T=0.2sec[/tex]

Generally the Period is given as

 [tex]T= 2 * 0.2 = 0.4[/tex]

Therefore difference in frequency dF

 [tex]dF=\frac{1}{T}[/tex]

 [tex]dF=\frac{1}{0.4}[/tex]

 [tex]dF=2.5Hz[/tex]

Answer:

1.5kg

Explanation:

Given data

mass m1= 2.5kg

mass m2=??

velocity of mass one v1= 1.5m/s

velocity of mass two v2= 4.1m/s

common velocity after impact v= 2.5m/s

Let us apply the formula for the conservation of linear momentum for inelastic collision

The expression is given as

m1v1+ m2v2= v(m1+m2)

substitute

2.5*1.5+ m2*4.1= 2.5(2.5+m2)

3.75+4.1m2= 6.25+2.5m2

collect like terms

3.75-6.25= 2.5m2-4.1m2

-2.5= -1.6m2

divide both sides by -1.6

m2= -2.5/-1.6

m2= 1.5 kg

Hence the second mass is 1.5kg

Solution :

We know,

Distance,

[tex]$S=ut+\frac{1}{2}at^2$[/tex]

[tex]$S=ut+0.5(a)(t)^2$[/tex]

For the first 20 ms,

[tex]$S=0+0.5(220)(0.020)^2$[/tex]

S = 0.044 m

In the remaining 30 ms, it has constant velocity.

[tex]$v=u+at$[/tex]

[tex]$v=0+(220)(0.020)[/tex]

v = 4.4 m/s

Therefore,

[tex]$S=ut+0.5(a)(t)^2$[/tex]

[tex]$S'=4.4 \times 0.030[/tex]

S' = 0.132 m

So, the required distance is = S + S'

                                              = 0.044 + 0.132

                                              = 0.176 m

Therefore, the tongue can reach = 0.176 m or 17.6 cm

Answer:

The total distance is 0.176 m.

Explanation:

For t = 0 s to t = 20 ms

initial velocity, u = 0

acceleration, a = 220 m/s^2

time, t = 20 ms

Let the final speed is v.

Use first equation of motion

v = u + at

v = 0 + 220 x 0.02 = 4.4 m/s

Let the distance is s.

Use second equation of motion

[tex]s = u t + 0.5 at^2\\\\s = 0 + 0.5 \times 220 \times 0.02\times 0.02\\\\s = 0.044 m[/tex]

Now the distance is

s' = v x t

s' = 4.4 x 0.03 = 0.132 m

The total distance is

S = s + s' = 0.044 + 0.132 = 0.176 m

The concept of this question can be well understood by listing out the parameters given.

The purpose is to determine the spring constant.

Let us assume that the two blocks are Block A and Block B.

At point A on block A, the initial velocity on the block is zero

i.e. u = 0

We want to determine the time it requires for Block A to reach the table. The can be achieved by using the second equation of motion which can be expressed by using the formula.

[tex]\mathsf{S = ut + \dfrac{1}{2}gt^2}[/tex]

From the above formula,

The distance (S) = 30 cm; we need to convert the unit to meter (m).

The acceleration (g) due to gravity = 9.8 m/s²

∴

inputting the values into the equation above, we have;

[tex]\mathsf{0.3 = (0)t + \dfrac{1}{2}*(9.80)*(t^2)}[/tex]

[tex]\mathsf{0.3 = \dfrac{1}{2}*(9.80)*(t^2)}[/tex]

[tex]\mathsf{0.3 =4.9*(t^2)}[/tex]

By dividing both sides by 4.9, we have:

[tex]\mathsf{t^2 = \dfrac{0.3}{4.9}}[/tex]

[tex]\mathsf{t^2 = 0.0612}[/tex]

[tex]\mathsf{t = \sqrt{0.0612}}[/tex]

[tex]\mathbf{t =0.247 \ seconds}[/tex]

However, block B comes to an instantaneous rest on point C. This is achieved by the dropping of the block on the spring. During this process, the spring is compressed and it bounces back to oscillate in that manner. The required time needed to get to this point C is half the period, this will eventually lead to the bouncing back of the block with another half of the period, thereby completing a movement of one period.

By applying the equation of the time period of a simple harmonic motion.

[tex]\mathbf{T = 2 \pi \sqrt{\dfrac{m}{k}}}[/tex]

where the relation between time (t) and period (T) is:

[tex]\mathsf{t = \dfrac{T}{2}}[/tex]

T = 2t

T = 2(0.247)

T = 0.494 seconds

[tex]\mathbf{T = 2 \pi \sqrt{\dfrac{m}{k}}}[/tex]

By making the spring constant (k) the subject of the formula:

[tex]\mathbf{\dfrac{T}{2 \pi } = \sqrt{ \dfrac{m}{k}}}[/tex]

[tex]\Big(\dfrac{T}{2 \pi }\Big)^2 = { \dfrac{m}{k}[/tex]

[tex]\dfrac{T^2}{(2 \pi)^2 }= { \dfrac{m}{k}[/tex]

[tex]\mathsf{ T^2 *k = 2 \pi^2*m} \\ \\ \mathsf{ k = \dfrac{2 \pi^2*m}{T^2}}[/tex]

[tex]\mathsf{ k =\Big( \dfrac{(2 \pi)^2*(51 \times 10^{-3})}{(0.494)^2} \Big) N/m}[/tex]

[tex]\mathbf{ k =8.25 \ N/m}[/tex]

Therefore, we can conclude that the spring constant between the two 51 g blocks held at a distance 30 cm above a table as a result of instantaneous rest caused by the compression of the spring is 8.25 N/m.

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Answer:

A. 9280.78 moles.

B. 37123.12 g.

Explanation:

We'll begin by calculating the volume of the spherical balloon. This can be obtained as follow:

Diameter (d) = 6 m

Radius (r) = d/2 = 6/2 = 3 m

Pi (π) =3.14

Volume (V) =?

V = 4/3πr³

V = 4/3 × 3.14 × 3³

V = 4/3 × 3.14 × 27

V = 113.04 m³

Next, we shall convert 20°C to Kelvin temperature. This can be obtained as follow:

T(K) = T(°C) + 273

T(°C) = 20°C

T(K) = 20°C + 273

T(K) = 293 K

Next, we shall convert 200 KPa to Pa. This can be obtained as follow:

1 KPa = 1000 Pa

Therefore,

200 KPa = 200 KPa × 1000 Pa / 1 KPa

200 KPa = 2×10⁵ Pa

A. Determination of the number of mole of He in the spherical balloon.

Volume (V) = 113.04 m³

Temperature (T) = 293 K

Pressure (P) = 2×10⁵ Pa

Gas constant (R) = 8.314 m³Pa/Kmol

Number of mole (n) =?

PV = nRT

2×10⁵ × 113.04 = n × 8.314 × 293

22608000 = n × 2436.002

Divide both side by 2436.002

n = 22608000 / 2436.002

n = 9280.78 moles

B. Determination of the mass of He.

Mole of He (n) = 9280.78 moles

Molar mass of He = 4 g/mol

Mass of He =?

Mass = mole × molar mass

Mass of He = 9280.78 × 4

Mass of He = 37123.12 g

a) The mass flow rate through the nozzle is 0.27 kg/s.

b) The exit area of the nozzle is 23.6 cm².

a) The mass flow rate through the nozzle can be calculated with the following equation:

[tex] \dot{m_{i}} = \rho_{i} v_{i}A_{i} [/tex]

Where:

[tex]v_{i}[/tex]: is the initial velocity = 20 m/s

[tex]A_{i}[/tex]: is the inlet area of the nozzle = 60 cm²  

[tex]\rho_{i}[/tex]: is the density of entrance = 2.21 kg/m³

[tex] \dot{m} = \rho_{i} v_{i}A_{i} = 2.21 \frac{kg}{m^{3}}*20 \frac{m}{s}*60 cm^{2}*\frac{1 m^{2}}{(100 cm)^{2}} = 0.27 kg/s [/tex]  

Hence, the mass flow rate through the nozzle is 0.27 kg/s.

b) The exit area of the nozzle can be found with the Continuity equation:

[tex] \rho_{i} v_{i}A_{i} = \rho_{f} v_{f}A_{f} [/tex]

[tex] 0.27 kg/s = 0.762 kg/m^{3}*150 m/s*A_{f} [/tex]

[tex] A_{f} = \frac{0.27 kg/s}{0.762 kg/m^{3}*150 m/s} = 0.00236 m^{2}*\frac{(100 cm)^{2}}{1 m^{2}} = 23.6 cm^{2} [/tex]

Therefore, the exit area of the nozzle is 23.6 cm².

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a) Mass flow rate through the nozzle: 0.265 kilograms per second, b) Exit area of the nozzle: 23.202 square centimeters.

We determine the Mass Flow Rate through the nozzle and the Exit Area of the nozzle by means of the Principle of Mass Conservation. A nozzle is a device that works at Steady State, so that Mass Balance can be reduced into this form:

[tex]\dot m_{in} = \dot m_{out}[/tex] (1)

Where:

[tex]\dot m_{in}[/tex] - Inlet mass flow, in kilograms per second.

[tex]\dot m_{out}[/tex] - Outlet mass flow, in kilograms per second.

Given that air flows at constant rate, we expand (1) by dimensional analysis:

[tex]\rho_{in} \cdot A_{in}\cdot v_{in} = \rho_{out}\cdot A_{out}\cdot v_{out}[/tex] (2)

Where:

[tex]\rho_{in}, \rho_{out}[/tex] - Air density at inlet and outlet, in kilograms per cubic meter.

[tex]A_{in}, A_{out}[/tex] - Inlet and outlet area, in square meters.

[tex]v_{in}, v_{out}[/tex] - Inlet and outlet velocity, in meters per second.

a) If we know that [tex]\rho_{in} = 2.21\,\frac{kg}{m^{3}}[/tex], [tex]A_{in} = 60\times 10^{-4}\,m^{2}[/tex] and [tex]v_{in} = 20\,\frac{m}{s}[/tex], then the mass flow rate through the nozzle is:

[tex]\dot m = \rho_{in}\cdot A_{in}\cdot v_{in}[/tex]

[tex]\dot m = \left(2.21\,\frac{kg}{m^{3}} \right)\cdot (60\times 10^{-4}\,m^{2})\cdot \left(20\,\frac{m}{s} \right)[/tex]

[tex]\dot m = 0.265\,\frac{kg}{s}[/tex]

The mass flow rate through the nozzle is 0.265 kilograms per second.

b) If we know that [tex]\rho_{in} = 2.21\,\frac{kg}{m^{3}}[/tex], [tex]A_{in} = 60\times 10^{-4}\,m^{2}[/tex], [tex]v_{in} = 20\,\frac{m}{s}[/tex], [tex]\rho_{out} = 0.762\,\frac{kg}{m^{3}}[/tex] and [tex]v_{out} = 150\,\frac{m}{s}[/tex], then the exit area of the nozzle is:

[tex]\rho_{in} \cdot A_{in}\cdot v_{in} = \rho_{out}\cdot A_{out}\cdot v_{out}[/tex]

[tex]A_{out} = \frac{\rho_{in}\cdot A_{in}\cdot v_{in}}{\rho_{out}\cdot v_{out}}[/tex]

[tex]A_{out} = \frac{\left(2.21\,\frac{kg}{m^{3}} \right)\cdot (60\times 10^{-4}\,m^{2})\cdot \left(20\,\frac{m}{s} \right)}{\left(0.762\,\frac{kg}{m^{3}} \right)\cdot \left(150\,\frac{m}{s} \right)}[/tex]

[tex]A_{out} = 2.320\times 10^{-3}\,m^{2}[/tex]

[tex]A_{out} = 23.202\,cm^{2}[/tex]

The exit area of the nozzle is 23.202 square centimeters.

Answer:

the density of the salt water is 1030 kg/m³

Explanation:

Given;

radius of the cylindrical pool, r = 2 m

depth of the pool, h = 1.3 m

specific gravity of the salt water, γ = 1.03

The atmospheric pressure, P₀ = 1.013 x 10⁵ Pa

Density of fresh water, [tex]\rho _w[/tex] = 1000 kg/m³

The density of the salt water is calculated as;

[tex]Specific \ gravity \ of \ salt\ water \ (\gamma _s_w) = \frac{density \ of \ salt \ water \ (\rho_{sw})}{density \ of \ fresh \ water \ (\rho_{w})} \\\\1.03 = \frac{\rho_{sw}}{1000 \ kg/m^3}\\\\\rho_{sw} = 1.03 \times 1000 \ kg/m^3\\\\\rho_{sw} = 1030 \ kg/m^3[/tex]

Therefore, the density of the salt water is 1030 kg/m³

Answer:

P = -1 D

Explanation:

For this exercise we must use the equation of the constructor

       / f = 1 / p + 1 / q

where f is the focal length, p and q is the distance to the object and the image, respectively

The far view point is at p =∞  and its image must be at q = -100 cm = 1 m, the negative sign is because the image is on the same side as the image  

        [tex]\frac{1}{f} = \frac{1}{infinity} + \frac{1}{-1}[/tex]

         f = 1 m

         P = 1/f

          P = -1 D

Answer: [tex]53\ rev/min[/tex]

Explanation:

Given

angular speed of wheel is [tex]\omega_1 =530\ rev/min[/tex]

Another wheel of 9 times the rotational inertia is coupled with initial wheel

Suppose the initial wheel has moment of inertia as I

Coupled disc has [tex]9I[/tex] as rotational inertia

Conserving angular momentum,

[tex]\Rightarrow I\omega_1=(I+9I)\omega_2\\\\\Rightarrow \omega_2=\dfrac{I}{10I}\times 530\\\\\Rightarrow \omega_2=53\ rev/min[/tex]

Answer: (d)

Explanation:

Given

15 W is equivalent to 60 W light that is, it save 45 W

So, for 4 hours it is, [tex]4\times 45=180\ W.hr[/tex]

For 30 days, it becomes

[tex]\Rightarrow 180\times 30=5400\ W.hr\\\Rightarrow 5.4\ kWh[/tex]

Thus, [tex]5.4\ kWh[/tex] is saved in 30 days

option (d) is correct.

Answer:

The final pressure in bar will be "[tex]\frac{10}{3} \ Bar[/tex]".

Explanation:

As we know,

PV = nRT

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

then,

⇒ [tex]\frac{2 \ bar}{300 \ K} = \frac{P_2}{500 \ K}[/tex]

⇒ [tex]P_2=(\frac{2}{300}\times 500 )Bar[/tex]

        [tex]=\frac{10}{3} \ Bar[/tex]

Thus the above is the correct answer.

Answer: hello  some of your values are wrongly written hence I will resolve your question using the right values

answer:

stiffness =  1.09 * 10^-6 N/m

Explanation:

Given data:

Length ( l ) = 16 m

radius of wire ( r ) = 3.5 m

mass ( m ) = 5kg

Distance stretched (  Δl ) = 4 * 10^-3 m ( right value )

average bond length ( between atoms ) = 2.3 * 10^-10 m ( right value)

first step : calculate the area

area ( A ) = πr^2 = π * ( 3.5)^2 = 38.48 m^2

        γ          = MgL / A Δl

                    = [ (5 * 9.81 * 16 ) / ( 38.48 * (4.3*10^-3) ) ]

                    = 784.8 / 0.165 = 4756.36 N/m^2

hence : stiffness =   γ  * bond length

                           =  4756.36 * 2.3 * 10^-10  = 1.09 * 10^-6 N/m

Answer:

EMF = 51.01 Volt

Explanation:

A 50-turn coil has a diameter of 15 cm. The coil is placed in a spatially uniform magnetic field of magnitude 0.500~\text{T}0.500 T so that the plane of the coil makes an angle of 30^\circ30 ​∘ ​​ with the magnetic field. Find the magnitude of the emf induced in the coil if the magnetic field is reduced to zero uniformly in 0.100~\text{s}0.100 s

We have,

Number of turn in the coil, N = 50

The diameter of the coil, d = 15 cm

Radius, r = 7.5 cm = 0.075 m

Initial magnetic field, [tex]B_i=0.5\ T[/tex]

The plane of the coil makes an angle of 30° with the magnetic field.

The magnetic field reduced to zero in 0.1 seconds

We need to find the emf induced in the coil. We know that, emf is equal to the rate of change of magnetic flux. So,

[tex]\epsilon=\dfrac{BNA\cos\theta}{t}\\\\\epsilon=\dfrac{0.5\times 50\times \pi \times 0.075\cos(30)}{0.1}\\\\\epsilon=51.01\ V[/tex]

So, the induced emf in the coil is 51.01 V.

Answer:

The total distance, side to side, that the top of the building moves during such an oscillation is approximately 0.291 meters.

Explanation:

Let suppose that the building is experimenting a Simple Harmonic Motion due to the action of wind. First, we determine the angular frequency of the system ([tex]\omega[/tex]), in radians per second:

[tex]\omega = 2\pi\cdot f[/tex] (1)

Where [tex]f[/tex] is the frequency, in hertz.

If we know that [tex]f = 0.18\,hz[/tex], then the angular frequency of the system is:

[tex]\omega = 2\pi\cdot (0.18\,hz)[/tex]

[tex]\omega \approx 1.131\,\frac{rad}{s}[/tex]

The maximum acceleration experimented by the system is represented by the following formula, of which we estimate amplitude of the oscillation:

[tex]r\cdot g = \omega^{2}\cdot A[/tex] (2)

Where:

[tex]r[/tex] - Ratio of real acceleration to free-fall acceleration, no unit.

[tex]g[/tex] - Free-fall acceleration, in meters per square second.

[tex]A[/tex] - Amplitude, in meters.

If we know that [tex]\omega \approx 1.131\,\frac{rad}{s}[/tex], [tex]r = 0.019[/tex] and [tex]g = 9.807\,\frac{m}{s^{2}}[/tex], then the amplitude of the oscillation is:

[tex]A = \frac{r\cdot g}{\omega^{2}}[/tex]

[tex]A = \frac{(0.019)\cdot \left(9.807\,\frac{m}{s^{2}} \right)}{\left(1.131\,\frac{rad}{s} \right)^{2}}[/tex]

[tex]A \approx 0.146\,m[/tex]

The total distance, side to side, is twice the amplitude, that is to say, a value of approximately 0.291 meters.

Answer:

X = 10.8387 cm²/s

Explanation:

In this exercise, you're required to convert a value from one unit to another.

Converting 42 ft²/hr to cm²/s;

Conversion:

1 ft² = 929.03 cm²

42 ft² = X cm²

Cross-multiplying, we have;

X = 42 * 929.03

X = 39019.26 cm²

Next, we would divide by time in seconds.

1 hour = 3600 seconds

X = 39019.26/3600

X = 10.8387 cm²/s

Answer:

Explanation:

Given that:

diameter of the circular plates = 16.8 cm

mass of the plastic bead = 1.8 g

charge q = -4.4 nC

From above, the area of the circular plates is:

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

[tex]Area = \pi (\dfrac{d}{2})^2[/tex]

[tex]Area = \pi (\dfrac{16.8}{2*100} m)^2 \[/tex]

Area = 0.022 m²

Thus, as the plastic beads glide between the two plates of the capacitor, there exists a  weight acting downwards while the weight is balanced by the force of the plates acting upwards.

Hence, this can be achieved only when the upper plate is positively charged.

b)

Recall that

Force (F) = qE

where;

F = mg

mg = qE

[tex]E = \dfrac{mg}{q}[/tex]

[tex]E = \dfrac{1.8*10^{-3}*9.8}{4.4*10^{-9}}[/tex]

E = 4.0 × 10⁶ N/C

From the electric field;

[tex]E = \dfrac{\Big(\dfrac{Q}{A}\Big)}{e_o}[/tex]

[tex]4.0*10^{6} = \dfrac{\Big(\dfrac{Q}{0.022}\Big)}{8.85*10^{-12}}[/tex]

[tex]4.0*10^{6}*8.85*10^{-12} = {\Big(\dfrac{Q}{0.022}\Big)}{}[/tex]

[tex]Q= 4.0*10^{6}*8.85*10^{-12}*0.022[/tex]

Q = 7.788 × 10⁻⁷ C

Q = 779 nC

Answer:

d = 30kg/cm³

Explanation:

d = m/v

d = 1080kg/(3cm*4cm*3cm)

d = 30kg/cm³

Answer:

960 nm

Explanation:

Given that:

wavelength = 640 nm

For the second (2nd) dark spot;  the order of interference m = 1

Thus, the path length difference is expressed by the formula:

[tex]d sin \theta = (m + \dfrac{1}{2}) \lambda[/tex]

[tex]d sin \theta = (1 + \dfrac{1}{2}) 640[/tex]

[tex]d sin \theta = ( \dfrac{3}{2}) 640[/tex]

dsinθ = 960 nm

This seems to be incomplete, as we do not have any information about the magnetic field surrounding the wire, but we can answer in a general way.

We know that for a wire of length L, with a current I, and in a magnetic field B, the force can be written as:

F = L*(IxB)

if we define the right as the positive x-axis, and knowing that the current flows to the right, we can write:

I = i*(1, 0, 0)

And the field will be some random vector that can't be parallel to the current because in that case, we do not have any force.

To find the direction of the force, which will tell us the direction in which the wire deflects or moves, first, we need to point with our thumb in the direction of the current, in this case, to the right.

Now, with the hand open, using the tip of our other fingers we point in the direction of the magnetic field.

For example, if the magnetic field is in the positive z-axis, we will point upwards.

Now the palm of our hand tells us in which direction the force is applied.

This is the right-hand rule.

For example, in the case that the current goes to the right and the magnetic field is upwards, we could see that the force is to the front.

Answer:

the correct one is d

Explanation:

The filament of the bulb fulfills the law of ohm

          V = i R

indicate that the filament resistance increases with temperature, as the voltage remains constant if the resistance of the filament increases the current should decrease,

When examining the different statements, the correct one is d

Answer:

thanks for da 5points hoi

Explanation: thanks dawg

There can be uncertainty in calculating the wavelength of a laser light  due to experimental errors

All measurements have an uncertainty, in the case of direct measurements the uncertainty is equal to the precision of the given instrument.

Uncertainty  means the range of possible values within which the true value of the measurement lies.

The deviation  in the value of the measured quantity from the actual quantity or true value is called an error

(a) For the calculation of wavelength of laser light , the sources which can lead to uncertainty are

1. least count of measuring instruments like spectrometer or interferometer

2. Parallax error in the measurement

3. Error in identifying the order of fringes

4.. unable to identify the accurate  reading of Vernier or circular scales present in the measuring instruments.

5. Propagating errors

The least count of a measuring instrument is the smallest and accurate value in the measured quantity that can be measured by instrument.

When you have derived variables, that is, when measurements are made with different instruments, each with a different uncertainty, the way to find the uncertainty or error is that  all the errors add up. which increases the uncertainty

b. The uncertainty in measurement due to  least count depends on the instrument used for measurement f wavelength. A  Michelson's

interferometer has the least count of .0001mm. whereas spectrometer has a least count of 0.5⁰. Hence uncertainty in the measurement by Michelson's interferometer is very less as compared to any other instrument.

C. The maximum uncertainty arises due to the least count , as all other errors can be minimized by taking an average value of many observations but the least count of an instrument do not change so uncertainty within the least count arises.

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#SPJ2

The work done by [tex]\vec F[/tex] along the given path C from A to B is given by the line integral,

[tex]\displaystyle \int_C \mathbf F\cdot\mathrm d\mathbf r[/tex]

I assume the path itself is a line segment, which can be parameterized by

[tex]\vec r(t) = (1-t)(-2\,\vec\imath + 5\,\vec\jmath) + t(4\,\vec\imath+7\,\vec\jmath) \\\\ \vec r(t) = (6t-2)\,\vec\imath+(2t+5)\,\vec\jmath \\\\ \vec r(t) = x(t)\,\vec\imath + y(t)\,\vec\jmath[/tex]

with 0 ≤ t ≤ 1. Then the work performed by F along C is

[tex]\displaystyle \int_0^1 \left(6x(t)^3\,\vec\imath-4y(t)\,\vec\jmath\right)\cdot\frac{\mathrm d}{\mathrm dt}\left[x(t)\,\vec\imath + y(t)\,\vec\jmath\right]\,\mathrm dt \\\\ = \int_0^1 (288(3t-1)^3-8(2t+5)) \,\mathrm dt = \boxed{312}[/tex]

Answer:

the masses of the two stars are; m₁ = m₂ = 4.92 × 10³⁰ kg

Explanation:

Given the data in the question;

Time period = 6 months = 1.577 × 10⁷ s

orbital speed v = 64000 m/s

since its a circular orbit,

v = 2πr / T

we solve for r

r = vT/ 2π

r = ( 64000 × 1.577 × 10⁷ ) / 2π

r = 1.6063 × 10¹¹ m = ( (1.6063 × 10¹¹) / (1.496 × 10¹¹) )AU = 1.0737 AU

Now, from Kepler's law

T² = r³ / ( m₁ + m₂ )

T = 6 months = 0.5 years

we substitute

(0.5)² = (1.0737)³ / ( m₁ + m₂ )

0.25 = 1.2378 / ( m₁ + m₂ )

( m₁ + m₂ ) = 1.2378 / 0.25

( m₁ + m₂ ) = 4.9512

m₁ = m₂  = 4.9512 / 2 = 2.4756 solar mass

we know that solar mass = 1.989 × 10³⁰ kg

so

m₁ = m₂ = 2.4756 × 1.989 × 10³⁰ kg

m₁ = m₂ = 4.92 × 10³⁰ kg

Therefore, the masses of the two stars are; m₁ = m₂ = 4.92 × 10³⁰ kg